Maths Demo Class 01| Next Officers Batch 2.0 - SSC CGL 2027 I RATIO PROPORTION I Jyotiprakash Sir

追加: 2026-06-04

[00:00:00]Hello and very good morning everyone. In this class, we are going to start actual mathematics for your competitive examination. This class is all about ratio and proportion where we will be covering the level one. Level one means we will be building your fundamental around this topic. Now understand one thing very clearly. This topic is the most important topic in terms of its utility in your whole competitive examination journey. Whether you go for SSC, banking or railway without this subject it is impossible. So understand each and everything because this is where you will need to ensure that you are fundamentally so good that you are able to implement all the tricks and tips through this class through this chapter and you can use the same thing in upcoming chapters as well. Okay. So let's start the class. So basically today what we are going to learn is about the fundamentals of ratio and proportion. So this class will be lighter but it will be of a lot of information. Okay. So first thing is we have seen ratios like somewhere we see like it is 2x3 or in some places it is written this like this or in some places it is written like this or in some places it is written like this or some places we have seen it something like this. Yes or no? So all these sort of ratios we have seen in our entire education journey. So we'll just sum it up all these things. Basically ratio tells us about comparison between what? Comparison between two quantity. Okay. So let's say two and three these are two individual quantities. What is their comparison between them? Now when we are comparing between two quantities we write it like this. So let it write it like this a is to b. Now when a is what the first b is what the second number or I can write it as a by b. So in terms of mathematics a is known as antecedent b known as precedent. This value this wording has no value in your examination but you need to understand this. Now in some cases also you have seen some things are written like this. A is to b is to c is to d. This means what? This means a by b is equal to c by d. Okay.

[00:02:28]Now what this a and d signifies? A and d signifies the extremes the extremes of both the ratios. and B and C signify signifies the mean of both the ratio.

[00:02:43]Now based on this when we'll be solving proportion proportion means ratio comparison between or relation between two ratios. So when we will be learning proportion in detail through our this chapter in type two we'll understand how relation between two ratios work. Okay.

[00:03:05]So having this clarity let's understand what are the types of ratio we will be dealing through the class. So the first type that we will be dealing is that is known as equivalent ratio. What it is equivalent ratio. Now equivalent means it is somewhere related to equal but it is not exactly equal. Right? So equivalent means what? Let's say one ratio is 2x3.

[00:03:35]One ratio is 2x3. If I multiply two on the numerator or the anticedant and I multiply two in the denominator or the precedent, this is known as anticedant.

[00:03:49]This is known as precedent also. This is known as the numerator and this is known as the denominator. Okay. So if I multiply this, I'll get what? 4x 6. So the value of 2x3 is actually equal to the value of 4x 6. So what I can say 2x3 is the simplest form of 4x 6 or 2x3 in place of 2x3. If I write 2x3 * 5002 * 5002 it will be what sir it will be 104. It will be sir 1506. So if I say 104x506 it is equal to 2x3 or I can say 2x3 is the simplest form of this ratio. So equivalent ratio means what?

[00:04:43]Equivalent ratio means two or multiple ratios.

[00:04:53]Two or multiple ratios have equal value. Equal value. The value of 2x3 is equal to 4x 6 is equal to 104 by 1506. and the simplest form. Clear? So you can find the simplest form of this ratio and still you can find the same value or same calculation in your exam or in the question. Clear? Yes or no? So if I say I have a ratio that is written like this that 18 by 27. So if I solve it, if I divide 18 by 9 and 27 by 9, I will get 2x3. So 2x3 is the simplest form of 18x 27. And on the same time I can say 2 18 by 27 is the equivalent ratio of 2x3. Clear?

[00:05:54]Sorted. Now the second thing that is known as inverse ratio. Now here most of the problem arises because student do not feel confident about this inverse ratio. Now inverse means what? The first and foremost thing inverse means we see the mirror image right. Inverse actually works like this. So in the mirror after our left hand may look like our right hand. Our right hand may look like our left hand. Right? So inverse ratio this happens like this. If a is to b is a ratio or you can say a by b is a ratio.

[00:06:32]Inverse of this ratio will be b is to a or b by a or I can mathematically write inverse of a by b is equal to 1 by a by b. When this is written like this, the denominator will go to the upper set and the numerator will be the denominator.

[00:07:01]So this is how inverse ratios are written. Clear everyone? So see I know if you are a repeater you may find this is boring but for the beginner those who are those who have fear for mathematics they need to learn all these things because these are the crucial points which will be covered in type three type two where we'll be dealing with difficult level of questions. Okay. Now third type of ratio that is known as duplicate ratio. Now this duplicate does not signify what this ratio is all about. The duplicate ratio means if a ratio is in the method a is to b duplicate value or duplicate ratio of a is to b is a² is to b². Let's say we have a ratio.

[00:07:54]For an example, the ratio is 8 is to 9.

[00:07:58]So it duplicate ratio will be 8² is to 9² that is equal to 64 is to 81. Clear?

[00:08:07]Sorted. So this is how we can write the duplicate ratio. Now the fourth part subduplicate ratio. What it is subduplicate ratio. Now what is this subduplicate ratio means? Sir, subduplicate ratio means if a ratio is in method A is to B.

[00:08:27]If I have to find out the subduplicate ratio of A is to B, it will be square root of A is to square root of B. Now what is this square root?

[00:08:40]How do we find the square root? If you do not know how to find the square root, go check out the speed math calculation video series available in SSC monk YouTube channel. Okay. So through that you need to cover all the things only you need to give 3 hours or less than 3 hours to complete that whole series and through that your calculation will be completed and this is the most important thing that you need to do before you start with the class. before we start with the course. Okay. So let's say we have a ratio of 25 is to 36. So what will be the subduplicate value sir?

[00:09:22]Square root of 25 is square root of 36 that is equal to 5 is to 6. So 5 is to 6 is the square root of 25 and 36. So subduplicate value of 25 is to 36 is equal to 5 is to 6.

[00:09:44]We will go slowly. We'll learn each and everything slowly and at the same time you need to understand remember all these facts. Okay. Next fifth part that is known as triplicate ratio. And why I am telling you all these things because you will see direct questions but in a difficult manner from this ratio part. triplicate ratio means if a ratio is in format a is to b then this can be written as triplicate ratio of it is written as aq is to bq clear so let's say we have a ratio of 4 is to 5 so what is the triplicate ratio of it 4 cq is to 5 cq 4 cq means what 64 5 cq means what 125. Yes or no? Clear. Sorted everyone.

[00:10:40]Perfect. Now sixth and the last part of this types of ratio that is known as subdicate. Now what happened in subduplicate? In subduplicate we used to take the square root. In subdicate we will be taking the cube root. What?

[00:10:57]We'll be taking cube root. Now how to find out cube root? Again go and complete the speed math calculation series if you haven't yet. So it will be cube root of a is 2 cube root of b.

[00:11:12]Let's say we have a number that is 64 is to 125. So this ratio if I have to find out the sublicate ratio of this ratio it will be cube root of 64 is to cube root of 125 that is equal to cube root of 64 means 4 because 4 multiplied three times gets me 64 and 125 cube root is 5 because 5 multiplied three times will get me 125. So this is how all the types of ratios we will be covering. Is it clear sorted? Yes or no? Perfect. Now we will deal with the question and we'll learn things through the questions.

[00:11:58]Okay. So first questions that comes from this type of this topic is basic questions related to ratio. Now how this basic question looks and how are we are going to solve this question? Let's learn it. Okay. So let's say one ratio is given A is to B that is equal to 2 is to 3. Another ratio is given B is to C C that is equal to 3 is to 5. So what is the value of A is to B is to C. If it says like this then what we can do? We will write it like this. A B and C. Okay. Three ratios are there.

[00:12:38]Yes or no? Yes. First ratio is 2 is to 3. Second is 3 is to 5. We'll write it like this. Then we'll draw a line over here. Our first job is to ensure that both these parts should be equal.

[00:12:54]Both this number should be equal. Now here both the numbers are equal. So I will directly write two here, three here, five here. So the value of a is two, value of b is three, value of c is five. So the ratio of a is to b is to c is 2 is to 3 is to 5 that is equal to this. This means I can write a by b is equal to 2x3, b by c is equal to 3x 5, a by c is = 2x 5, c by a = 5x2, c by b is equal to 5x3, b by a = 3x2. Why? And how I'm writing it? because I find out the value of A is 2, value of B is three and value of C is five. From that I can directly write if I'm asking about C by A, what is the value of C? Five. What is the value of A? Two. If I ask about C by B, what is the value of C? Five. What is the value of B? Three. If I ask you about what is the value of B by A, what is the value of B? Three. What is the value of A?

[00:14:02]Two. Clear? So this is how it is. Now if a number is written like this that a b c over here it is 2 3 6 and 7. If it is written like this then what sir here B and C has to be equal. In order to make this equal what I need to do? I need to take the LCM of 3 is to 6. And I have told you how to calculate the LCM. So LCM of 3 and 6 will be six. Now if I have to LCM is six. So how much I should multiply with three so that I will get six sir two. Now for this whole thing I have to multiply two. Okay. So now 2 2's are 4 2 3's are 6. So both will be six and seven over here. So a is 4 b is 6 c is 7. This is one way to solve it.

[00:14:56]Another way the most common way that everyone uses in the paper is let's say a here b here c here 2 3 6 and 7. So the first thing is you multiply these two and you write it over here 2 into 6. The second thing is you multiply these two 3 into 6 18 you write it here. Third is you multiply this two and you write it here. Let me write it 3 is to 6. Okay. 3 + 6. And here it will be 3 + 7. Now all this is what? 12. This is 18. This is 21. Now here this ratio is in a huge label. Right? We have to ensure that this is in the simplest possible format.

[00:15:43]So what will be the simplest form of this?

[00:15:47]We have to trim it down or we have to divide all these number by a single number so that we'll get a smaller value of this. Sir if I divide it by 2 it is not possible because 21 by 2 is not possible. So if I divide it by 3 it will be 3 4 are 12 3 6 are 18 3 7 are 21. Now what we got? 4 6 7. Can we divide all these three numbers further by any other number than 1? No. So what will be the ratio of a is to b is to c when a is to b is 2x 3 and b is to c is 6x 7. It will be 4 is to 6 is to 7. Now if I ask you here in this ratio what is the value of C by A? You will write sir C is equal to 7. A is equal to 4. If I ask you what is the value of B by A. You will write sir 6 by 4 because B value is 6. A value is four. Clear? Sorted. So this is how we find the ratios. It does not matter.

[00:16:49]Okay. How many ratios? What type of ratios are there? We will be able to find it this way. Clear everyone?

[00:16:57]Sorted. Next.

[00:17:00]A is to B and C is to D is given. What we should do now? See, A is to B is given 2 is to 3.

[00:17:12]C is to D is given 3 is to 5. Here there is no relation between A and C given or A and D given or B and C given or B and D given. Right? So if in any ratio there is no correlation available or can be established if in any ratio. If in any ratio there is no correlation available or no correlation can be established the final value can not be determined.

[00:18:08]This will be in shorter form written as C and D cannot determine. So answer option D. Here we cannot find the value because we do not know what is the ratio or what is the relation between B to C or B to D or A to C or A to D apart from the relation between A and B and C and D. Okay. Now it is written as 3 A is equal to 3 B that is equal to 3 C.

[00:18:42]Now how to solve it? Understand one thing. Whenever you are encountering questions like this 3 A is equal to 2 B is equal to 5 C. You do not have to panic. First thing you need to take care of is take out these two that you can write 3 a is equal to 2 b or you can say a divided by b is equal to two here three will come to the lower part is equal to 3. So what is the ratio of a is to b 2 is to 3. Yes or no? You got the idea or not? So this is the first part you need to understand properly. You need to understand properly. Now same way if I write 2 B is equal to 5 C. I will write B divided by C is equal to 5 / 2. So what is the value of P? What is the value of C? Got it? Now what is the ratio? 2 is to 3.

[00:19:48]What is the ratio? 5 is to2. So it is 2 is to 3. It is 5 is to2. What I'll do?

[00:19:54]Either I will make this equal or I'll multiply. 2 5 are 10. 3 5 are 15 3 2's are 6 Now can I solve it further? No. So what will be the ratio? 10 is to 15 is to 6. Answer option D. Clear?

[00:20:10]Got it?

[00:20:12]Resolved yes or no. So this is how you can solve such questions. Okay. And these sort of questions I am giving you for your practices also. You need to practice it and get better. Nothing is difficult. Understand one thing. It is all about understanding the basics properly so that you can deal it in the right manner. Okay. Now if it is written as a is to b is to c is equal to 1x 2 is to 1x 3 is to 1x 5 then find the value of a b c. Now what it is written a b c but these are in fractions 1 by 2 1x 3 1x 5. Now in order to eliminate these fractions or convert these fractions into integers I need to do what? I need to multiply a something that is equal in all the cases. A same number I should multiply here so that I can get the answer. Now in order to do that I will always take the LCM of 2 3 and 5. Now see 2 3 and 5 are prime numbers. So LCM will be 2 into 3 into 5 that is equal to 2 3 are 6 into 5 is equal to 30. So if I multiply 30 over here I'll get the right answer. How? 2 15 are 30.

[00:21:37]3 10 are 30. 5 6 are 30. So what is the ratio? 15 is to 10 is to 6.

[00:21:47]So this is the ratio. So what is the ratio? 15 is to 10 is to 6. This cannot be further simplified. So this will be the final answer. Clear? Sorted. Got the idea? Next. If it is written like this, a by b value is equal to 2 is to 3. B by C value is equal to 3 is to 5 and C by D value is equal to 4 is to 7. So what will be the ratio of A is to B is to C is to D. We do not have to worry at all.

[00:22:18]See A here B here C here D here. A is to B is given 2 is to 3 B is to C given 3 is to 5 C is to D given 4 is to 7. Now we need to ensure that these two are equal. These two are equal and at the same time these are in the similar pattern. These two are in the similar pattern. So we'll do double multiplication over here. What we'll do double multiplication over here. Now see two will be dropped to two because no changes over here. Three equal so it will be dropped to three. No change here. If there was some changes here, we would have solved it first and we'll write it down. Now five and four is here. So what will happen? We have to make these two equal. So what we'll do?

[00:23:11]5 4 LCM 20. So four will be multiply here. So if I multiply four over here, four 5 are 20. 4 3's are 12. Yes or no?

[00:23:21]So if this is 12, this should be multiply by 4 because this has to be 12.

[00:23:26]So if this is multiply by 4 4 3 12 4 2 will be 8. Yes or no? Yes. And now if four 5s are 20 here also 4 5 20 should happen otherwise the whole ratio won't work. So 5 is to 7 is equal to 35. So what is the ratio now? 8 is to 12 is to 35 that is equal to a is to b is to c is to d. So answer 8, 12, 20 and 35. Clear what we did. Let me explain it again. In the first place we do one thing that we write each and everything down. Okay.

[00:24:08]Now we started over here. Here we saw that we have to ensure that five and four are equal. So how to make it equal?

[00:24:15]The LCM is 20. So if I multiply four over here, if I multiply five over here, it will be 20. Perfect. Now if I'm multiplying four over here in this ratio I have to multiply four in the numerator and in the denominator as well. So if I multiplying four over here it will be 12. But in this it is three it is 12. So I have to make this also 12. So I have to multiply four over here. Now if I'm multiplying four in the denominator I have to multiply four in the numerator. So 4 into 2 is equal to 8. 4 into 3 12. 4 into 3 12 12 here. 4 into 520 5 into 420 here. Now if I'm multiplying five in the numerator over here I should multiply 5 in the denominator as well. So 5 into 7 is equal to 35. And that is how we got our final value that is 8 is to 12 is to 20 is to 35 that is the final value of this question. Clear? Next.

[00:25:15]If it is written x = 1 by 2 y = 1 by 3 z then what is the value of x is to y is to z. Now that see we have to find out x y z right now it has given x = 1 by 2 into y or I can write x / y is equal to 1 by 2.

[00:25:44]>> [snorts] >> Similarly, it is written y = 1 by 3 into z or I can write y by z is = 1 by 3. Now understand if x is = 1, y is equal to 2 as for the ratio here if y is 1, z is 3.

[00:26:05]So what will be the ratio of? See two here, one here. So I have to multiply two over here. So it will be 2 2 1 1 2 into 3 is equal to 6. So what is the ratio? 1 is to 2 is to 6 that is equal to option C. Clear sorted yes or no. So this is how we can solve the questions easily. I hope now you do not have any confusion. Next x is to y is to z= 2 is to 3 is to 5. Then what is the value of 4x² + y² + 3 z². Now see what I told you when it is written as X Y Z is equal to 2 3 and 5. This means zed value is 5, Y value is 3 and X value is equal to 2. So 4 x² + y² + 3 z² can be written as 4 into 2² + 3² + 3 into 5² that is equal to 4 into 4 + 3² is = 9 + 3 into 5 square is equal to 25 that can be written as 4 into 4 is equal to 16 + 9 3 into 25 is equal to 75 sir. 16 + 9 is equal to 25 + 75. 25 + 75 is equal to 100. Answer option what?

[00:27:32]Answer option 100. Not here. So what we need to do if 100 is not there. Here I think a word is number is missing. So answer will be 100. Clear? Sorted. Next.

[00:27:47]116 is divided into three parts which are in the ratio 1 is to 1x 3 is to 1x4 sir three parts means let's say one part is a another is b another is c the ratio is 1 1x 3 1x 4 sir one can be written as 1 by 1 also yes or no if a number is in integer its denominator is always one clear now what I need to do I need to take care of the LCM what will be the LCM 4 is to 3 that is equal to 12. So I'll multiply 12 over here 12 over here and 12 over here. 1 12 are 12 3 4 are 12 4 3's are 12. So what is the ratio now?

[00:28:29]12 is to 4 is to 3. That means out of 116 if I divide 116 into different difference part 12 part will be go to A four parts will go to B three parts will go to C. Yes or no? So in total how many parts I am making sir? I am making 12 + 4 + 3 that is equal to 19 parts. So I am making 19 parts of 116.

[00:29:03]So one part of 116 is equal to 116 divided by 90. Clear?

[00:29:14]Yes or no? So four part value will be equal to what? 116 by 19 into 4. Yes or no? Yes sir. If I solve this this will be close to 196 114. Yes or no? Yes. So this will be 6 something. Yes or no? So 4 into 6 will be 24 something or close to 25. So answer will be 25. Yes or no? Got it? So what exactly we are doing when a number is divided into different parts we find out the parts then we add the total part to get the final value and from that we can get the answer clear. Next a by b is equal to c by d is equal to e by f that is equal to 2x3. So it is written a by b is equal to c by d is equal to e by f that is equal to 2x3. This means a by b is equal to 2x3 c by d is equal to 2x3 e by f is equal to 2x3. This is the most important part you need to understand.

[00:30:31]Okay. Now it is asking 3 a + 2 c + 4 e divided by 3 b + 2 d + 4 f is equal to what? Sir 3 into a that is equal to 2 + 2 into c that is equal to 2 + 4 into e that is equal to 2 divided by 3 into b that is equal to 3 2 into d that is equal to 3 + 4 into f that is equal to 3. So I can write 2 3 2's are 6 2 2's are 4 4 2's are 8 divided by 3 3's are 9 2 3's are 6 4 3's are 12 sir 6 4 10 + 8 18 divided by 9 6 15 + 12 27 now 18 and 27 they both can be divided by 3 or 9. So if I divide it by 9 it will be 9 2 are 18 9 3's are 27. So the value is equal to 2 is by 3 or 2 is to 3. Clear?

[00:31:42]So this is how we can solve all the easy oneliner questions this way. Is this clear to everyone? You got you are getting the idea right? How we are solving these questions. Next P is to Q is equal to 3 is to 4. Q is to R is equal to 4 is to 7. So what is the value of P + Q is to Q + R is to R + P. Now see P here Q here R here P is to Q is equal to 3x 4. So I'll write 3 over here 4 over here. Q is to R is 4 is to 7. So what will be the ratio? So 3 is to 4 is to 7. That means P value is 3, Q value is 4, R value is 7. So I can write P + Q is 2. Q + R is 2. R + P is equal to 3 + 4 because that is the value of P + Q. Q + R will be 4 + 7 and R + P will be 7 + 3. So 3 + 4 is equal to 7 is to 4 + 7 is equal to 11 + 7 + 3 is equal to 10. So what is the ratio? 7 is to 11 is to 10.

[00:32:59]This cannot be simplified further. So the answer will be option B. So this is how we can solve the questions of basics of ratio and proportion. Clear? Next. 7 x + y divided by 7 x - y is equal to 7 by 2. So let's say a number is written as 7 x + y / 7 x - y is equal to 7 by 2.

[00:33:32]So in order to do that there are two ways. So first way is you cross multiply here and here. So 2 into 7 x + y is equal to 7 into 7 x - y.

[00:33:51]This means this means 4 2 into 7 x 14 x + 2 into y 2 y that is equal to 7 into 7 49x - 7 into y 7 y sir 49x 14x sir 49x if 14x will come to this side this will be - 14x that is equal to 7 y will come to this side but minus sign so this side it will be plus that will be 7 y + 2 y so I can Write 49x - 14x is equal to 35x is equal to 7 + 2 9 y or I can write x / y is equal to 9 by 35. Can this be solved further? No. So the ratio will be 9 is to 35. Answer option clear.

[00:34:45]If you do not want to extend this whole thing in this method then there is a monk method. Okay. What it is monk method and this method you need to understand if any number is written like this a + b divided by a minus b is equal to c by d then I can write a by b and 2 * here and 2 mult*ly here that means 2 a by 2 b is equal to C + D / C minus D or I can write A by B is equal to C + D by C minus D. This is one formula. Another formula is if a by b is equal to c by d I can directly write a + b by a minus b is equal to c + d by c minus d. If you remember these two things, you can solve this sort of ratio questions. Now see, it is written 7 x + y / 7 x - y is equal to 7 by 2. Now see if I take 7 x= a, y = b. So it is a + b by a minus b that is equal to c by d. So I can write directly a by b is equal to 7 c + d / c minus d or I can write 7 x by y is equal to 9 by 5 or I can write 7 over here. So it will become to the denominator x by y is equal to 9 by 35. So in both the cases we got the answer. Here we have to do a lot of multiplication. Here we'll be saving a lot of saving a lot of time because of monk method. Is this clear to everyone? You need to understand what I am saying why I am saying and now you should not be worried about how this whole you know tricks is working. I just told you the tricks or a property of this ratio in order to learn it. You do not have to implement it right now. In level two we will be using this exclusively. I will tell you how to use it. But for now, do not stress over.

[00:37:16]Just learn each and everything simply, slowly and gradually. Okay? Because we are building the foundation. In any house, if you try to, you know, fasten the process of building the foundation, the whole house won't be that strong, right? So, this is how math works. Your foundation should be slow, steady, and really strong. If that is strong then you can take care of a lot of things. If that is not strong then it will be really really difficult for you to cope up for other things. Okay. And for these basic parts we are taking longer at a period of time. After that the timing will be really slow. Okay.

[00:37:55]Next 5x + 3 y divided by 5x - 3 y is = 7 by 3. So I can write 5x + 3 y / 5x - 3 y is = 7 by 3. Either I can cross multiply or I can write 5x by 3 y is equal to 7 + 3 divided by 7 - 3. That means 5x by 3 y is equal to 10 by 7 - 3 4. Yes or no?

[00:38:34]Yes. Now 5 / 10. 10 divided by 5 is equal to 2 and 2 2 are 4. So I can write x by y = 3 will go to the upper part and the lower part it is 2 that is equal to 3x2. Answer option. Clear [clears throat] in certain question it may ask find the value of y byx but in the examination because of the pressure you may write it 3 is to2 but in the question if it is written as y byx you have to take 2x3 this is what you guys need to understand. Okay. Next. A by b is equal to b by c is equal to c by d. Then what is the value of a b by c? See a b c d over here. a is equal to what? 3 is to 4. B is equal to what? 2 is to 7. C and d is equal to what? 5 is to2. Clear?

[00:39:34]Yes. Now one thing understand if I multiply two over here it will be 2 is 2 to 4. So both these value will be four and this part will be 7 2's are 14. So this is 14 this is five. So in order to make both of these equal what I need to do? I need to five multiply five over here and I need to multiply 14 over here. Yes or no? This is what you need to understand and this is where most of the students get confused because this is no longer seven. This is already 2 into 7 is equal to 14. Clear?

[00:40:11]Yes or no? Yes. Now this number is no longer four. It is now 5 into 4 is equal to 20. So you have to make it 20. So what you will do? You will multiply it by five. This is how your whole thing will be correct. Now understand 3 into 5 is equal to 15 4 into 5 is equal to 20.

[00:40:33]So both of these will be 20 because 2 into 2 4 into 5 20. Now 7 into 2 14 into 5 is equal to 70 or I can write 14 into 5 is equal to 70 and 14 into 2 is equal to 28. So what is the value of a 15, b 20, c 70, d 28. Clear? Now it is asking a b by c d. This means 15 into 20 divided by 70 into 28. Clear? Yes or no?

[00:41:10]Yes. So we can write 0 0 gone 2 14 are 28. This can be written as 15 by 14 7 are 98. So answer is equal to option D. Clear what we did, how I solve it, that is more important over this section. If I do the right thing in this section, everything will be perfect ahead. Got the idea? Clear how we are solving each and every part of all these things. Now next type two questions based on proportion. Okay, we'll learn how proportion works. What are the most important parts? Okay. And we'll learn through each and every question. Okay. Now find the third proportion to 12 6<unk>5. Now see here I'll give you the introduction to proportion. Okay. Let me quickly change the color. Now whenever proportion is written how many types of proportion will come?

[00:42:18]First type will come that will be known as mean proportion.

[00:42:23]mean proportion of a is to b that is equal to square root of a into b. Let's say there are two number one is 8 or 2 and another is 8. So mean proportion will be what 2 into 8 16 square root of 16 is equal to 4. So for an example mean proportion of 2 and 8 will be square root of 2 into 8 square root of 16 that is equal to 4. So this is one.

[00:42:59]Second third proportion of A and B. Now understand third proportion is what? A is to B is to C.

[00:43:16]We are you are finding C over here. This can be written as A by B is equal to B / by C. Yes or no? Or this can be written as B² by A is equal to C because C will come to this side. B into B is equal to B square divided by A= C. So the third proportion can always be written B² by A. Let's say for an example there are two numbers 2 and 3. Third proportional to 2 and 3 will be what? Sir a is 2 b is 3. So b² that means 3² divided by a that is equal to 2. So I can write 9 by 2. So what is the third proportion to 2 and 3?

[00:44:02]9 by 2 or you can write 4 is 4 4.5.

[00:44:06]Clear? So this is how third proportional is written. Now if it asks what is the fourth proportion to A, B and C. So fourth proportional means what? A is to b is equal to c is to d. That means I can write a by b is equal to c by d. Here I am finding out the fourth proportional d value. So I can write d is equal to b into c divided by a. So if it asks what is the fourth proportional to 2 3 and 4 I can write see here it is a here it is b here it is c. So d value will be equal to b into c divided by a 2 2's are 4 3 into 2 is equal to 6. So what is the fourth proportion? Fourth proportion is equal to 6. So this is how you can find out the proportional values. You can find out the proportional values. Okay. Now here in this question it is asking find the third proportion to 12 and 6<unk> 5.

[00:45:23]Sir 12 here is my A 6<unk>5 here is my B. So what will be the third proportion?

[00:45:32]So third proportion or C value will be B² divided by A that means 6<unk>5 into 6<unk> 5 by 12 6 2 are 12 2 3's are 6<unk> 5 into<unk> 5 will be 5 into 3 that is equal to 15. So what is the third proportional value 15 clear? This means 12 / 6<unk>5 is equal to 6<unk>5 / 15. If you solve it, you will get the same answer. You want to see it? Let's understand. Sir, 6 2. So this left side will be 2x roo<unk> 5. Yes or no? Yes. Sir, here it is written as roo<unk> 5. Okay.

[00:46:24]Sir here 6 into<unk> 5 divided by I can write 3 into 5 is equal to 15 sir 3 2's are 6<unk>5 into roo<unk> 5 is equal to 5 so I can write<unk> 5 5 / roo<unk> 5 is equal to roo<unk> 5 so here in the left side it is 2x roo<unk> 5 on the right sheet also it is 2x roo<unk> 5 so hence the answer we find is proved so this is how third proportional works clear next find the fourth proportional to 0.2412 0.6 and 20. Now a is equal to what?

[00:47:02]0.2412 b is equal to what? 0.6 c is equal to what? 20. So the value of d is equal to b into c divided by a because we are finding out the fourth proportional. Clear? So b value is equal to what? 0.6 6 C value is equal to what 20 the A value is equal to what 0.2412 2 412. Now see I have to drop the decimal.

[00:47:31]So it will be 6 by 10 into 20 divided by 2 412 divided by how many numbers are there after decimal? 4. So it will be 1 4 * 0. Yes or no? 10 2. So this can be written as 6 into 2 = 12 * 1 2 3 4 * 0 divided by 2 412. Yes or no?

[00:47:56]Clear? Got the idea? Now understand 12 2's are 24 0 12 1's are 12. So this value is equal to what? 2011 into this much. So this is approximately equal to 50. So the answer will be approximately equal to 50. See I am taking the approximate value because here the defined value will be in decimals. So there is no point of solving the whole thing to decimal because everything is in approximate values. Okay. Next. What is the mean proportional between 64 and 4096? Sir, mean proportion is equal to square root of 64 into square roo<unk> of 4096. Now if you do not know to find out how we are calculating square root of bigger numbers you can check out speed math calculation series video and that will help you immensely. Now see square root of 64 is equal to 8 and square root of 4096 is equal to 64. So 8 into 64 is equal to 512.

[00:49:09]Answer option A. Clear? Sorted. Next.

[00:49:14]What is the ratio of third proportional to 0.4 and 0.8 to the mean proportional between 13.5 and 0.24? So what it is asking third proportional to mean proportional.

[00:49:31]Okay. So what is the third proportional to this sir? This is a this is b. So this will be b² by a divided by mean proportional between 13.5 into 0.24 yes or no? Yes.

[00:49:54][snorts] So I can write sir 8 divided by 10 8 / 10 divided by 4 by 10 because this is how decimal here sir 10 10 gone 4 2 8 So the upper part will be 16 by 10 divided by here it will be square root of 13.5 can be written as 135 by 10 into 24 by 100 yes or Now what we can do now sir 16 by 10 on the opposite side here I can write 135 is equal to 15 into 9 * 24 is equal to 4 into 6 divided by 10 into 100 square root of the whole thing 5 3's are 15 5 2's are 20 2 are 4 Now on the upper part it is 16 by 10 divided by sir 3 into 2 6 so it will be 9 into 6 into 6 / 100 square root of this whole thing. So I [snorts] can write this 16 by 10 divided by 9 square root is 3 square root of 6 and 6 36 is equal to 600 square root is equal to 10. So 10 lower side 10 lower side gone. This can be written as 16 by 18 or this can be written as 2 8 are 6 2 9 are 18. Answer option 8 is to 9.

[00:51:24]Clear? Sorted. So this is how we can solve these questions easily without worrying too much. Okay. Next. The ratio compounded of 4 by 4 is to 5 and subduplicate of a is to 9 is 8 is to 15.

[00:51:44]Compound ratio is what?

[00:51:54]and c is to d is equal to a into c by b into d. So here it is saying the ratio compounded of 4 by 5 and subduplicate of a by 9 is equal to 8 is to<unk> 15. That means 4 into subduplicate of a means square root of a divided by 5 into square roo<unk> of 9 that is equal to 4<unk> a divided by 5 into 3 and this value is equal to what? 8 by 15. Now say 5 33 by 15 15 gone. So I can write 4 2's are 8. So square root of a is equal to 2. If square root of a is 2 if I square both side it will be a = 2² that is equal to 4. Answer option c. So this is how we got the idea. First thing we need to understand is what is the compounded ratio of a is to b and c is to d. So that is a * c by b * d. So from that we got the answer clear. Next dash is to 4 is equal to 48 is to 16. So it is written as dash by 4 is equal to 48 by 16. So 16 3's are 48. So here I do not know something. So that is equal to 4 into 3 that is equal to 12. Answer option A. Quite easy question in terms of proportion. Yes or no? This symbolize equal to this ratio is equal to this ratio. That is what you need to understand properly. Okay. Next.

[00:53:40]Same way 10 divided by something is equal to 24 by 36. Now if I divide it by 6 it will be 6 4 are 36 6 are 6 or 2 2's are 4 2 3's are 6 or 2 5 are 10 3 into 5 is equal to 15 or I can write this question mark is equal to 5 into 35 answer option C clear sorted next find the third proportional to 5 3 and 12 now see this is A this is B. This is C.

[00:54:20]Here third proportional asked. So here this analogy will be wrong.

[00:54:27]Why? First is first, second is second, third is missing. That means C is unknown. This will be D. This is what you need to understand. So I know A by B is equal to C by D. So I can write a by b means 5 by 3 is equal to c unknown divided by d that is equal to 12 3 4 are 12 c value is equal to 5 into 4 that is equal to 20. Answer option C. Clear?

[00:55:02]This is how we will decode the question and find the question. If we understand this basic properly, we will be able to understand whichever proportional it ask. Clear? Sorted. Next. If a b, b c, x and c² are in proportion, then find the value of x. See if they are in proportion, I can write a b by b c is equal to x by c². Yes or no? Yes. Now see B on the both side gone. Here C will cross out one C. So X value will be A into C. Yes or no? So what is the value?

[00:55:48]X value is equal to A C. We are going really simple. We are just simplifying here each of thing because if it is A into B on the upper side B is multiplied on the lower side B is multiplied. So they they can cross each other. Okay. If here C square is written if here C is written C 1 C will be gone. So only C will be written because C² is equal to C into C. So 1 C taken out only one C remaining. So X is equal to A into C.

[00:56:15]Clear? Next. If two numbers are 4 and 8.

[00:56:19]First proportional to these numbers is what? First proportional means a is unknown. So I can write a by b is equal to b by c or I can write a = b² by c or b² means 4 into 4 divided by c8 4 2 are 8 2 2 4. So a value is equal to 2. Answer option two. See whether it is first or second or third or fourth. If we know what it is all about, we will be able to solve it.

[00:57:00]Clear? Next. What is the third proportional of numbers 4 and 48? Now see 4 and 48 means 4 is equal to A. 48 is equal to B.

[00:57:12]So I can write C is equal to 48²Rided by A. 42 are 48. 48 into 10 is equal to 480. 48 2 are 96 so this is equal to 576 answer option C clear sorted next what is the ratio of mean proportional between 4.8 and 10.8 and third proportional to 0.4 and 2.4. So what we are going to find mean proportional to third proportional ratio. So mean proportional means what 4.8 8 and multiply by 10.8 square root of that divided by third proportional means a here b here 2.4 into 2.4 by 0.4 4 sir here I can write 48 by 10 into 108 by 10 square roo<unk> of 8 divided by 24x 10 into 24x 10 divided by 4x 10 now 110 110 gone 4 6 are 24 okay now here what I can do sir here 48 is there so uh let's say this is equal to 16 into 3. Okay. So let's write it down. 16 into 3 is equal to 48 / 10 into sir 10 is to 8. Sir this can be written as 36 into 3 / 10 square root of that divided by here it is 6 into 24 that is equal to 144 divided by 10. Clear? Now understand one thing 16 square root is 4 36 square root is 6 3 into 3 9 square root is 3 divided by 10 into 10 100 square will be 10 divided by 144 by 10 so 10 10 gone now 4 3's are 12 2 4 6 are 34 6 are 36 3 2's as six. So on the upper part nothing is there. So it will be one. On the lower part it will be two. So the ratio will be 1 by 2 or I can write 1 is to2.

[00:59:41]Answer option B. Clear. Only simplification.

[00:59:45]We are not doing anything fancy over here. We are simplifying things in the right manner. Clear? Next. Find the compound ratio of the following. So compound ratio means 1 into 3 / 2 into 5 that is equal to 3x 10. Answer option A.

[01:00:07]Clear? Next. Find the compound ratio of the following. So here it will be 0.45 into 1 by 9 divided by 0.55 into 4x5. Yes or no? Yes. Now see here I can write 45 by 100 55 by 100. So I can take out directly the decimal. Okay. Now 5 11 9 5. So I can write 5 into 15 divided by 11 into 4 44. So what is the compounded ratio? 5 is to 44. We are only simplifying the whole thing. Okay.

[01:00:48]Now find the duplicate ratio. So duplicate ratio means 14 squared is to 17 squared. 14 square is equal to 196 17 squar is equal to 289.

[01:01:03]So the ratio is 196 is to 289. Clear?

[01:01:08]Next. Find the subduplicate ratio. Sir duplicate means square root of 16 is to square root of 25. So square root of 16 is equal to 4. square root of 25 is equal to 5. So the ratio is equal to 4 is to 5. Do not click 5 is to 4 in terms of getting you know confused or in terms of you know in the examination you are going very rush. Okay keep it simple keep it sorted. Next find the triplicate ratio. triplicate means 3 cq is to 5 cq.

[01:01:43]3 cq is to 5 cq can be written as answer option c also here the answer will be 3 cq is equal to 27 5 cq is equal to 125.

[01:01:54]So both a and c will be the answer.

[01:01:57]Remember this proper. Next find the sublicate.

[01:02:04]Now subdicate means cube root of 512 is 2. Cube root of 729.

[01:02:12]Now cube root of 512 is 8 because 8 cube is equal to 512. Cube root of 729 is 9.

[01:02:19]So ratio will be 8 is to 9. Now how I am able to answer this cube root and subcq root easily because of the speed math that enables us to calculate each and everything orally. So you have to practice it. That is why I'm keep on saying if you want to have a good hold over mathematics speed math is the first thing you should start with.

[01:02:46]You start with speed math then you learn the elementary things then you get into the course otherwise it will be difficult if you are not from a math background or if you fear mathematics okay next word based problems okay simple questions will be there how we need to you know deal those questions I'll let you know I will tell you okay the first question is the sum of money 4200 is distributed between Ammer and madan in the ratio of 9 is to5. This means what? Omar and madan are two guys.

[01:03:25]Omar is getting 9 part. Modern is getting five part. So how much is the total part? 9 + 5 is equal to 14 part.

[01:03:33]So this 14 part is equal to what? 4200 because 4200 has been distributed between and madan. Out of this 4200 nine part is going to Amar, five part is going to mother. This is how you need to break down the question. This is how you need to understand how to approach the question directly. Fine sir, if 14 part is equal to 4200, one part will be 4200 divided by 14. 14 3 are 42 3 into 100 is equal to 300. Sir if one part is equal to 300 mother s is equal to five part so it will be multiply by 300 because each part is 300 so 5 into 300 is equal to500 so what is the s of mother500 if it ask about amar you will multiply 9 into 5 300 so that will be equal to 2700 clear next a sum of 4,410 is distributed among sunny Bobby and Dhandra. Sunonny is getting three parts. Bobby is getting seven parts. Dhandra is getting eight parts.

[01:04:47]So what is the total part? 3 + 7 + 8 that is equal to 18 parts. And this 18 part is equal to how much money sir?

[01:04:56]4,410.

[01:04:59]Sir 18 part is equal to 4,410.

[01:05:02]So one part will be 4,410 by 18. Clear? Yes or no? Yes. Now it is asking about what is the value of sunny.

[01:05:12]Now see 9 2 are 18 9 4 are 36 9 9 are 81 0 2 2's are 4 2 4 are 8 2 5 are 10. So each part is equal to 245. So if each part is 245 sunny value will be 3 into 245 that is equal to 735 answer option D. Do not get confused in the calculation and mark wrong thing.

[01:05:45]Okay you need to mark it properly. Got it? Next. Three numbers are in the ratio 3 is to 4 is to 5. The sum of the largest and smallest equals the second that is equal to 52.

[01:06:04]Second and 52 find the smallest number.

[01:06:07]So what it is saying there are three numbers. First number, second number and third number. So first number is three, second number is four, five number, third number is five. So here I can write it is in the ratio 3x is to 4x is to 5x. Now it is saying sum of the largest 5x and sum of the smallest that means 5x + 3x is equal to the second number 4x + 52. Sir 5x + 3x is equal to 8x that is equal to 4x + 52.

[01:06:45]Or I can write 8x - 4x = 4x that is equal to 52. 4 13 are 52. So x value is equal to 52. Sir, if x value is equal to 50 sorry 13 sir if x value is equal to 13. So what is the smallest number sir? 3x. So 3x value will be 3 into 13 that is equal to 39. Answer option C. Clear? This [snorts] is how we deal with the basic questions. This is how we solve all the questions. Next. 120 students appeared in a test. Which of the following cannot be the ratio of failed to pass students?

[01:07:31]Now see fail plus past student should be equal to total number of students. Now students the numbers will be always in integer. Yes or no?

[01:07:49]Whole value will be there. It should be a whole number. Yes or no? Sir 3 + 5 is equal to 8. Sir 8 part is equal to 120.

[01:07:58]One part will be what? 120 by 8. Sir 8 1's are 8 8 5 are 40. So this is giving whole number. So this can be the this will represent the right number. Now 9 is to 1. So 9 + 1 is equal to 10. 10 part is equal to 120. Each part will be 120 by 10. That is equal to 12. So each part is a whole number. Perfect. Sir 5 + 7 that is equal to 12. So 12 means what?

[01:08:27]120. So 120 by 12 is equal to 10 parts.

[01:08:31]So the ratio is equal to what?

[01:08:36]in whole number. Perfect. Here sir, 5 is to 1. 5 is to 1 means total part 6 part is equal to 120. One part will be 20. So 20 into 500 20 into 1. So here all these things all these things will be the value of fail to pass numbers. Here you can say that fail should be less than pass. Nothing works like that. If here let's say it is equal to 3 is to 4 then it would have been total seven part seven part is equal to 120 means each part will be 120 by 7 this won't be a whole number so I could have said 3 is to 4 cannot be the ratio of fail to pass students okay but in the previous case everything was representing everything in a whole number okay so if only the ratio is not a whole thing then only I will be able to answer this question.

[01:09:37]Okay. Next. A sum of 13,950 is divided into now a sum of 13,950 is divided among A and B and C such that B gets double of A. C gets 50 less than B. What is the share of A? Now see B gets double of A.

[01:10:01]C gets 50 less than double of B. So 2 * B minus 50. But sir, B is equal to 2 A. So I can write 2 into 2 A - 50 is equal to C or I can write 4 A minus 50. Yes or no? Yes.

[01:10:20]But sir, I know here 13,950 is divided between A, B, C. That means whatever A get plus whatever B get plus whatever C get if I add all these I'll get 13,950.

[01:10:34]Yes or no? Yes sir. A value is equal to as it is B value can be written is equal to 2 A plus C value is equal to 4 A minus 15 that is equal to 13,950.

[01:10:45]Why I did it this way? So I will be able to find the value of A and from that I can find the value of B and C. Okay. Now 4 + 2 6 + 1 7 A is equal to 13,950 minus 50 will come to this side so it will be + 50 that is equal to 14,000. So 7 A is equal to 14,000 that means A is equal to 14,000 by 7 that is equal to 2,000. So what is the value of A? So share of A is equal to 2,000. If it ask about B it will be 2,000 into 2 that is equal to 4,000. If it ask about C, it will be 4,000 into 8,000 minus 50 that is equal to 7,950.

[01:11:29]And this is how we could have answered the question. Okay. Next, the product of two integers is 15 is to 15,75.

[01:11:41]The ratio is equal to 9 is to 7. If the first number is 9, second number is 7, I can write the numbers are in 9 x and 7 x. So there product means 9x into 7 x is equal to 1575.

[01:11:58]Yes or no? Yes. Now let's solve this. 9 1 are 9 6 7 9 7 are 63 4 5 9 5 are 45. Clear? Now 7 2's are 14 35 7 5 are 35. So I can write x into x that is x² is equal to 25. So the value of x is equal to square roo<unk> of 25 that is equal to 5. Answer what? Find the smaller number. sir smaller number is 7 x that means 7 x is equal to 7 into 5 that is equal to 35. Answer option B.

[01:12:38]Clear? Sorted. Got the idea how we are solving each and every question. how we are decoding the value and how we are writing it and how we are solving it.

[01:12:49]Clear? Next. If one number divided by another number gives 3x5 the difference is 28 then find the larger number. Now see let's say first number second number it is in 3x 5 or I can write 3x 5x their difference that means 5x - 3x is equal to 28 that means 2x is equal to 28 2 14 are 28 so x value is equal to 14. Sir if x value is equal to 14 larger number is 5x. So 5 into x is equal to 5 into 14 that is equal to 70. Answer option C.

[01:13:33]Clear. How we are dealing with each question that is important. How we are reading each question that is important.

[01:13:40]Okay. Next.

[01:13:43]Twice the square of a number. Uh this is eighth number. Okay. So I think this is a misprinting. So this is an eth number.

[01:13:51]Twice the square of a number is 6 * the other number. What is the ratio between first and second number? Let's say sir first number is x, second number is y.

[01:14:05]It is saying 2 * square of the number is equal to 6 * the other number.

[01:14:17]That means 2 3 are 6 or I can write y = x² by 3. Yes or no? Yes. So here it is written x by y. Yes or no? So I can write x by y is equal to x divided by x² by 3. Or I can write x will take out one power. 3 will go to the upper part that will be 3x. So x by y is equal to 3x. So we are unable to find the answer. So we will say we cannot find the value. We cannot find the value because here in the ratio x is there not one is there.

[01:15:04]So we will write we can't say we can't find the answer. Got the idea? Next questions based on coins. Now what will happen?

[01:15:17]This is a particular type. It is one of the favorite type of SSC. So you need to understand each and everything and learn how this thing is working. Okay. So it is saying in a box containing 1 rupee 50 pes 25. Now you just think when we were you know used to be child or when we used to you know in the school so whenever a relative was visiting us they used to uh pay us something right as a gesture of goodwill or you can say they used to like us being a child and they used to you know pay us like 5 rupees 10 rupees 20 rupees 50 rupees 100 rupees depending on how rich they are right so what we used to do we used to keep that in a box right so think about this so that box you have you have put one rupees is 50 pesa 25 pesa. I hope I mean most of you haven't seen even what is a 25 pesa coin look like or a 50 pesa coin look like but you have seen and you can imagine that you have a box and you have these many things and the ratio of 1 rupee is 1, 50 pesa is 2 and 25 pesa is 3.

[01:16:32]This is the ratio of what? Number of coins. This is the ratio of number of coins. So what is the total part? Sir 1 + 2 3 + 3 6. So total number of part is equal to six part. And this six part is equal to what? The number of 50 pesa coin is 80. That means two part is equal to 80. So each part will be 80 by 2 that is equal to 40. Yes or no? So if two part is 80, each part will be 80 by 2 that is equal to 40.

[01:17:07]That means how many one rupees coin sir?

[01:17:10]40. How many three 25 pesa coin? 3 into 40 that is equal to 120. Clear? Yes or no? So the exact number of coins is equal to what? 40 in one rupees 80 50 pesa 25 pesa 120. Now how much will be the value sir? The value will be 40 into 1 rupees coin plus 80 into 50 pesa coin plus 120 into 25 pesa coins. Sir 40 into 1 rupees is equal to 40 rupees. Sir 80 rupees of 50 pesa that will be 40 rupees because 250 pesa will get me what? 250 pesa will get me 80. So I can write 50 or 1 by 2 here in terms of rupees. Okay. So this will be 40. Sir 120 into 25 pesa sir 24 25 pesa makes 1 rupees. So I can write 25 pesa or 1x4 rupees directly because remember this 25 pesa is equal to 1x4 rupees 50 pesa is equal to 1 by 2 rupees. So in case of pesa you can directly multiply this rupees. So 120 into 1x4 is equal to 30 rupees. So total is 40 + 40 80 + 30 110. So how much rupees was there? What was the value in that box? So you have collected 110 rupees. Okay. So this is how we can deal with coins question. Next coin question.

[01:18:49]Sir, a 110 are contained in a box which consists of one rupee, 50 pesa and 25 pesa coins in the ratio of 1 is to 2 is to 3. So what is happening? Rupees 1 rupee 50 pesa can be written as 1x 2 rupees or 25 pesa can be written as 1x4 rupees.

[01:19:18]Yes or no? Yes.

[01:19:20]Now ratio of coins is equal to what? 1 2 3 or I can write 1 x 2x 3x yes or no. So value will be what? 1 into 1x that is equal to 1x 1x 2 into 2x that is equal to 1x2 into 2 2 gone that is equal to 1x 1x 4 into 3 that will be 3x 4x yes or no so what is the total value sir total value is equal to 1 + 1 2x + 3x 4x that can be written as 4 2 8 + 3 11 by 4x so this 11^ 4x this total value is equal to what? Sir this total value is equal to 110.

[01:20:12]This total value is equal to 110. If sir this total value is equal to 110. So I can write x is equal to 110 into 4 by 11 11 10 are 10. 10 into 4 is equal to 40.

[01:20:27]Sir if x value is equal to 40 x is what the value over here. So here the value will be 3x4 into 40 that is equal to 30 rupees. Sir here the value will be x into 40 40 rupees. Here the value will be x into 40 that is equal to 40 rupees. Yes or no? Yes. Now here x value is 14. So I can write x into 1 is equal to 40 coins over here.

[01:20:57]22x into 40 that means 80 coins over here. 3 into 40 that means 120 coins over here. Yes or no? Yes. That means if it ask how many 50 pesa coins are there?

[01:21:08]80 50 pesa coins are there. How many 25 pesa coins are there? 120 25 pesa coins are there. How many 1 rupees coins are there? 41 rupees coins are there. This is how you can answer the questions. Got it? So this is how we got the number of coins, the value of coins and the total value. What we did in order to find the total value, we multiply the value of each coin into the number of coins. So value of coins is equal to value of each coin multiply by number of coins. Clear?

[01:21:55]Next, a bag [snorts] contains coins of rupees 1 2 and 5 in the ratio 5 is to 10 is to 6 respectively. The total amount in the bag is 275.

[01:22:07]How many five coins are in the bag? Now see 1 2 rupees 5 rupees are there? Yes or no? Yes. How many one rupees are there?

[01:22:19]Five. How many two rupees are there? 10.

[01:22:21]How many five rupees are there? Six. So these are in 5x 10 x 6x. This is ratio of coins. So value will be what? Sir value will be 5x into 1 5x 10 x into 2 20 x 5 into 6x 30x that is equal to 30 + 20 50 + 5 is equal to 55x. But this 55x is equal to what? So total value is equal to 275.

[01:22:51]Sir that means 55 x is equal to 275 x value will be 275 by 55. You can directly write 55 5 are 275 or divided by 11 and you can get the answer. So 55 5 is equal to 275. So the value of x is equal to 5. So this will be 6 x mean 6 into 5 that is 30. 10 into 5 that is equal to 50. 5 into 5 that is equal to 25. So how many five rupees coins are there? Answer 35 rupees coins are there.

[01:23:21]Answer option A. Clear? Sorted. Got the idea? Next.

[01:23:28]The ratio of number of coins of 25 pesa, 50 pesa, 2 rupees and 5 rupees is equal to 5 431 respectively. If total amount of coins is equal to 28 285 then what will be the difference in number of coins between 25 pesa and 5 rupees. Now see 25 pesa I can write it as 1x4 rupees. Then 50 pesa I can write it as 1x 2 rupees. Then 2 rupees here and five rupees coins are here. Clear? What is the process? 5 4 3 1. This can be written as 5x 4x 3x and x. This is number of coins. What will be the value?

[01:24:16]sir value will be 5 into 1x 4 that means 5x 4x + 4 into 1x2 that means 2x 3 into 2 6 x 1 into 5 5 x. So this total is equal to 5x 4x + 6 to 8 + 5 13x sir 5 + 13 4 are 52 that means 57 by 4x is the total value sir 57 by xx 4 is equal to what sir it has given 57x 4x is equal to 285 sir I know 57 5 are 285 so the value of x is equal to 4 into 5 20 value of x is 20 sir Now it is asking the difference between 25 pesa number of coins and 5 rupees coins that means 5x - 1x that is equal to 4x that is equal to 4 into 20 that is equal to 80. So what is the difference number of coins? 80.

[01:25:18]This is what difference in number of coins we got the value yes or no. This is how we can solve the questions. Okay.

[01:25:30]Next. In a bag 10, 20, 50 nodes are kept in the ratio 1 is to 3 is to 5. If total value of money kept in the bag is 1920, what is the total number of 20 rupees note? Again simple question. There is a 10 rupees note, 20 rupees note, 50 rupees note. Number of nodes is equal to 1x 3x 5x. Sir value will be what? 10 into 1x that is equal to 10 x. Here 20 into 3x that is equal to 60x. 50 into 5 that is equal to 250x. So total value is equal to 250 + 70 that is equal to 320x.

[01:26:12]If I add all this I'll get 320x. This 320x is equal to 1 920 0 0 got 32 6 are 192. So the value of x is equal to 6. If value of x is equal to 6. What is the total number of node? 3 into 6 that is equal to 18. So how many 20 rupees nodes are there? 18 20 rupees nodes are there.

[01:26:37]Clear? Sorted. Next question based on proportion after addition and subtraction. Simple question will be there. We'll be dealing with simple simple question. So do not panic. It is saying what should be added to each term of the ratio 5 and 11 so that the ratio becomes 3 and 5. So a ratio is 5 by 11. If I add something to five and the same number should be added to x so that I'll be getting 3x 5. If I cross multiply I will get 5 into 5 + x is equal to 3 into 11 + x. That means 5 into 5 25 + 5x = 33 + 3x that can be written as 5x - 3x is equal to 33 - 25.

[01:27:34]So 2x value is equal to 33 - 5 is equal to 8. x value is equal to 8 by 2 that is equal to 4. So what is the value of x?

[01:27:44]So what is the number I am adding? Four I am adding to it. Now see this is a level one class. In the level one class wherever I think that you can handle the tricks I will tell you the tricks otherwise in level two we will be exclusively solving this question through tricks only. So do not panic.

[01:28:05]Okay. Next. What number should be added to each of the numbers so that the resulting are in proportion? Sir proportion means what? If I add 6 + something to 14 + something that ratio will be equal to 18 + something by 38 + something.

[01:28:29]Clear? Now here how to deal this question? So if I cross multiply over here it will be 13 into something then it 14 into something then it will be x² and x square and it will be too tough.

[01:28:41]Okay. So in order to do that first thing I can do what I can use the options because options are smaller. If I do not want to use that what I should do I should keep it simple. I will write 6 14 18 and 38. What is the difference between 6 and 18? 12. What is the difference between 14 and 38? 24. So I will write 6x4 one side and 12x 24 in another side. Now understand I will not simplify this. That is the first thing.

[01:29:19]I will simplify this difference only. 3 4 are 12 3 8 are 24 4 2 are 8 that is equal to 1 by 2. Clear sir what is the difference between 6 and 14? That is equal to 8. Now if the difference between 1 by two or whatever it is one how much I should multiply here so that it will be 8. So if I multiply 8 over here so that it will be 8. Yes or no?

[01:29:46]That means on the upper part it will be 1 into 8. On the lower part it will be 2 into 8 is equal to 16. So what is the ratio final ratio? 8 by 16. What is my primary ratio? 6x4. So how much I am adding in six so that I'm getting eight that will be two. How much I'm adding in 14 so that I'll get get 16 that is two.

[01:30:09]That means if I add two in all these numbers these numbers will be in the proportion. You want to see it sir 6 + 2 by 14 + 2 is equal to 18 + 2 by 38 + 2.

[01:30:24]This can be written as 8x 16 is equal to 20 by 40. 8 2's are 16 20 by 2's are 14 so 1 by 2 is equal to 1x2 yes or no answer so answer is two over here what I did first step one I took the difference of all these numbers then I took the first ratio I took the difference in the step two and here I took this difference ratio simplified it and I checked how can I get the same value over here. So I multiplied in the upper side and lower side and from that I get the difference of x in step three only in three steps you can find it. We'll try few questions and we'll get the answer. Okay next what number should be added to each of the numbers 10 202 16 34 so that the resulting are in proportion. Now 10 16 difference 6 20 to 34 difference 12. Now I'll take the first ratio that is equal to 10 by 22 and here it will be 6x2 that can be resolved into or simplified into 1x2. Sir what is the difference here? 12 sir what is the difference here? 1 sir if I have to make it 12 I should multiply 12 over here. So 12 in the numerator 12 multiplied in the denominator. So 12 into 2 is equal to 24. So here it is 10. Here it is 12. How much I should add sir? Two I should add so that I'll get the get everything in proportion. So what I'm adding sir I'm adding two so that all these numbers will be in proportion. Clear? Next how much is subtracted? As simple as that.

[01:32:09]If 16 and 19 is here, how much I am subtracting so that the ratio is 7 by 6 cross multiplied 96 - 6x is equal to 19 into 7 133x - 7 x sorry 133 - 7 x 7 x will come to this side. So 7 x - 6x is equal to x 133 - 6 is equal to 37. So if I'm subtracting 37 then I'll get the ratio in this. So let's try it. Sir 16 - 37 divided by 19 - 37. Sir 16 - 37 will be -21. 19 - 37 will be - 18. Yes or no? Yes sir. - will be gone. If I divide it by 3 3 7 are 21 3 6 are 18. So I'm getting the ratio 7 is to 6. Yes or no? So the answer is option B. So this is how we can directly solve these addition subtraction based questions. Okay. Now two numbers are in the ratio 5 by 7. On diminishing each by 40 they became the ratio of 17 is to 27.

[01:33:23]The difference of the number is what? So what is the difference between 5 and 7?

[01:33:28]Now five was the number 5x. I'm taking out 40 and there was a number 7 x I'm taking out 40 I am getting how much 17 by 27 this is what the question has given yes or no yes now it is asking me what is the difference between 7 x - 5x that is equal to 2x clear so I'll simply cross multiply 27 into 5 is equal to 135x - 27 into 4 is equal to 1080 that is equal to 17 into 7 1 9x - 17 into 40 680. So here I can write 135 - 119 is equal to 16x that is equal to 1080 - 680 that is equal to 400. Sir 4 are 16 400 are 400 425 is equal to 100. So x value is equal to 25. So 2x will be 2 into 25 that is equal to 50. So what is the difference between them sir? 50 clear sorted. There is a tricks to it that we'll learn in level two because if all the tricks will come in level one you will get confused. Okay. So there is a simpler way to solve this questions also. So we'll learn it in level two class. Okay. This will be the sixth question. Okay. Two numbers are in the ratio 9 is to 16. If both are increased by 40 the ratio becomes 2 is to 3. What is the difference between two numbers?

[01:35:03]That means 16x - 9x is equal to 7x we have to find. So 9x increased by 40 divided by 16x increased by 40 is now 2x 3. Okay. Now cross multiply 27x + 120 is equal to 32x + 80. 32x - 27x is equal to 5x. and 120 - 80 is equal to 40. 5 8 are 40. So what is the x is equal to 8. So 7 into 8 is equal to what? 56. So what is the difference between two number sir?

[01:35:37]56. Clear? Next questions based on income expenditure and saving and this sort of question you will see maximum number of questions are coming from this type in your profit and loss percentage also. Okay. So learn how we are dealing with these sort of questions. Now Surma earns 15,500 per month and his son earns 14,500 per month. What is the ratio of their annual income? Sir, Surma's annual income will be 15,500 * 12 ratio 14,500 * 12. Yes or no? Yes. Now if you calculate this and this and then you take the ratio, you are a fool because at the end 12 and 12 will be gone. 0 will be gone. So whatever it is the ratio will come here. 5 3's are 15, 5 1's are 5, 5 2's are 10, 5 9 are 45. So the ratio is equal to 31 by 29. Answer option A. But if you start multiplying the whole thing, 15,500 into 12, then you find the value, it will take around 10 seconds, then again 14,500 into 12, again 10 seconds, 20 seconds gone, then again the ratio. So it will be really hectic for all of you to do that. So instead of that you go through this step. Okay. Now Aina's monthly salary is 50,000. His monthly expenditure is 18,000. Radha's monthly salary is 60,000. His monthly expenditure is 24,000. What is the ratio of Radha's saving to Aina saving? Now understand one thing. Income is equal to expenditure plus savings. This is quite rhetoric. I know most of you know it. Also the same way I can write income minus expenditure is equal to savings or also I can write income minus savings is equal to expenditure. You need to remember this fact otherwise it will be tough for you. Okay. Now how many guys are there? One is Avinina and the girl is Radha. Okay.

[01:37:58]So there is an income thing. Then there is an expenditure thing. Then there is a saving thing. What is the income of Ainas? Ainas is earning 50,000. How much Radha is earning? 60,000.

[01:38:09]So Ainas is in level four job. Radha is in level five job. Okay. Now Avenas is spending 18,000.

[01:38:18]If I take out expenditure out of income, how much will be the saving? Sir 50 minus 38 is equal to 32,000. Radha is saving earning 60,000 but spending 24,000. So how much Radha is saving? Sir 36,000 she is saving. So what is the ratio of Radha saving to Aina saving?

[01:38:38]Sir 36,000 divided by 32,000 sir 0 0 gone 2 here it will be 18 here it will be 16 2 98 18 to 816 ratio is equal to 9 by8 answer option A clear so this is how we deal with the income expenditure and saving questions okay next monthly income of A and B are in the ratio 5 is to 4 their savings are in The ratio 4 is to 3. If each spend 700, find the monthly income. Now see A here, B here.

[01:39:17]Income expenditure saving. First thing is both are spending 700 and 700. Their income in the ratio 5x 4x they're saving in the ratio 43. Sir here I can directly write 5x - 700 divided by 4x - 700 is equal to 4 by3 yes or no income minus expenditure to the ratio of income minus expenditure is the ratio of saving this is the most important part to understand this is what the ratio of saving now cross multiply 15x - 2100 is equal to 16x - 2800 or I can write 16 - 15 is equal to x 2800 - 2100 is equal to 700. So what is the value of x 700? So it is asking what is the value of their saving. So 5x into 700 that is equal to 3500. 4x into 700 is equal to 2800. So what is the ratio sir? What is the value sir? C is the right way. Clear? Got the idea?

[01:40:31]Next. The ratio of income to expenditure of a family is 10 to 7. If expenditure is 11,900, find the seven. Sir, if income is 11, expenditure is 7, what will be the saving? 11 - 74. So, this seven part is equal to 1 900. So, each part will be 7 1 7 4 9 7 7 are 490. Sir if each part is 1,700 sav savings will be 4 into 17 that is equal to 6800. So answer option oh sorry this is 10. Okay so this will be three. So 17 into 3 is equal to 5100. Answer option A. Clear sorted. Next income of A B C are in the ratio of 475. The expenses of B uh A B C is 546. A saves for 400 out of 32. Find savings B and C. Now understand it is very clear. A here, B here, C here. A is 4, B is 7, C is 5. This is what? Income.

[01:41:46]Their expense is what? 5 4 6. Now savings unknown. Now what it say? A saves 400 out of 3,200.

[01:41:59]That means what sir? A income was 3,200 out of which he saves 400. So how much he has spent? 2800 he has spent. Clear everyone?

[01:42:14]Now sir four part is equal to 3200. Each part will be 3200 by 4. Sir 3,200 by 4 can be written as 800. That means B salary will be 7 into 800 that is equal to 5600.

[01:42:29]C salary will be 800 into 5 that is equal to 4,000. Clear? Now sir five part expenditure is equal to 2800. So each part will be 2800 by 5 that is equal to 5 5 are 25 30 3 0 5 6 are 30. So what is the base expenditure sir? 4 into 560 that is equal to 4 into 500 is 22,000 60 into 422 so 2240 is the expenditure now for C this expenditure will be what sir expenditure will be 6 into 560 sir 5 630 636 so this is equal to 3360 so what will be the saving 56 5600US 2240 sir 240 + 60 30 2300 3 2600 3,000. So 3,360 is the savings of B. So what [snorts] will be the savings of C? Sir, 60 + 40 is equal to 400. 400 + 60 is equal to 4,000. So savings of B is 3,360.

[01:43:35]C is 640. Answer option.

[01:43:39]Got the idea. Did you understand how we are doing this? It is simple. We just decoded that if A saves 400 out of 3200 out of means what? Out of his salary he will be able to save only right then we are able to solve the question. Clear?

[01:43:57]Sorted. Next. A and B have income in the ratio of 6 is to 7. Their expenditure in the ratio of 4 is to 5. If they save 2,000 and 18,000 what is B? 1,800 then what is B's income? Sir A here, B here.

[01:44:18]Income of A here, expenditure here, savings here. Sir, income of A 6X, income of B is 7X. Ratio of expenditure 4 is to 5. A is saving 2,000. B is saving 1,800. Sir, I can write 6X - saving is equal to expenditure 2. B's expenditure 7X - 1,800. So the ratio of expenditure will be 4x 5 yes or no? Yes.

[01:44:46]So if I cross multiply what I will get sir 30x - 10,000 is equal to 4728x - 7200. So I can write 30 - 28 2x is equal to 10,000 - 7,200 that is equal to 2800. So x value is equal to 28 by 2 that is equal to 1400. Sir if x value is equal to400 b income is 7 into,400 that is equal to 9,800 answer. So answer option c. Clear? Got the idea how we are solving this question. Yes or no? Next salaries of a b c are in the ratio of 3 is to 4 is to 7 after. So I'll keep this question for percentage class because you need to understand how percentage works. So in percentage class also we will be solving these sort of questions.

[01:45:42]Okay. So do not worry. So with this we are done with the first part level one of whole ratio and proportion. Now through this class you know all the ins and out of ratio and proportion. In the next class we will be covering the level two. And with level one and level two, you will be able to score 50 out of 50 in your tier one for sure because we have covered all types and all levels for your tier one. Level three is purely for tier 2 nature and most difficult questions are there in level three.

[01:46:18]Okay. So I hope you got the idea. Now go through the class notes then go through the practice sets. See you in the next.