APPSC IPO 2026 | Maths Lecture 6 | Percentages Tricks & Concepts | Industrial Promotion Officer

Ajouté : 2026-05-07

[00:00:00]Academy. Fine. So, in the last class, what we have completed, we have done with ratios.

[00:00:07]And I hope you are doing ample number of problems on this topic. Because you know that if you do if the subject like mathematics, unless you solve more number of problems in the chapter, you will not be able to excel this chapter. Okay, let me see. I think some sound is coming. Oh.

[00:00:24]Just Right. So, So, at least per chapter solve 30 to 40 problems. Minimum number of problems you need to solve it to understand or to grab the concept each concept of this chapter. I hope am I audible? Am I audible to all of you? Yes.

[00:00:47]Can you say it? Yeah, yeah, yeah. Fine.

[00:00:49]Am I audible? Fine. Yeah.

[00:00:51]So, so today we'll discuss about percentage. Uh last class I told you about ratios. And whenever talking about ratio, I told you the percentage is nothing but again a kind of ratio or when we compare two quantities, we use percentage. Fine. So, to understand percentage, let's take one very simple example to understand the concept of percentage.

[00:01:16]Fine. Now, for example, we have two ratios. Let me call one ratio is Uh let me change the color of the pen.

[00:01:26]Yeah.

[00:01:27]Suppose we have two ratios. One 6 by 10 and have another ratio 40 by 100.

[00:01:35]If I ask you to compare these two ratio, how will we do this?

[00:01:40]Right? What is meaning of 6 by 10? Out of 10, if you talk about marks getting by one student, out of 10, one student got six mark. And out of 100, the another student got 40 marks.

[00:01:53]Right? And I want to compare these two marks. How will I do this?

[00:01:56]So, to compare both the things, I'm trying to I'll do one thing. I'll make this also 100. So, to make denominator 100, I can say that this 6 by 10 is equivalent to 60 by 100.

[00:02:10]60 by 100. Other ratio is how much? 40 by 100. Now, I can compare both the things and we can say that 60 marks out of 100, one student is getting. Other student is getting 40 marks out of 100. Hence, this this performance of the first student is better than the performance of the second student. And fine. So, so basically, what we are doing, we are comparing two ratios, but taking the base as how much? 100.

[00:02:40]Right? So, can I say that the Again, when you compare two ratios by considering the base as 100, then we say that what? It is in the form of percentage. What is the meaning of percentage?

[00:02:57]Cent means 100. In each 100, how much?

[00:03:00]So, this is what? In the 100, we are getting 60. 100, we got 40. So, this we'll call as 60%. This value we'll call as 40%.

[00:03:11]Right? So, percentage is what? The another way of comparison where we make the denominator is equal to how much?

[00:03:17]100. Like let's take one live example.

[00:03:20]For example, suppose we talk about budget of a country. What I'm talking about here? The budget of a country is 3 T trillion.

[00:03:30]Budget of the country is how much? 3 trillion.

[00:03:36]Right? Now, among of this budget, they're giving how much? 8% they're allocating to education. What is the meaning of this?

[00:03:47]Total budget is 3 T 3 trillion and they're allocating how much? 3 8% to education.

[00:03:55]That means this complete 3 trillion value or the total budget will divide into 100 equal part. How many part will divide? 100 equal part. Out of 100 equal part, the eight part is what? Allocated to how much? Education.

[00:04:11]Clear? So, basically, whenever we talk about percentage, we divide a complete value into how many part? 100 equal part. Among of that, your percentage is suppose you talk about 10%.

[00:04:25]Right? What is meaning of 10%? 10 by 100 of the total quantity.

[00:04:32]What is the total quantity? Total quantity we'll consider as how much?

[00:04:35]100%. Fine.

[00:04:40]Now, so suppose we have 3%.

[00:04:44]What is meaning of 3%?

[00:04:51]This is nothing but out of 100, three is called as 3%. What is meaning of 5%? Out of 100, five is called as 5%. How will I write as? 5% will be equal to 5 by 100.

[00:05:04]Right? So, any total quantity may be the salary of a person is how much? 40,000.

[00:05:10]Right? So, if the salary of the person is 40,000, I'll call the total value as how much? 100% salary is 40%. Clear? So, 100% of a number is nothing but the number itself. I hope all of you are clear with what what we mean by percentage.

[00:05:24]Right? I think am I audible? Yes. Yes.

[00:05:28]Yeah.

[00:05:29]Fine.

[00:05:30]Then, suppose if I ask you what is the meaning of A percent?

[00:05:36]A percent means A divided by how much?

[00:05:40]100. Out of 100, A is called as how much? A percent. Clear? Then, next is suppose 100%. 100% is nothing but total value. So, the value of 100% will be equal to how much? 100 divided by 100, which is total value we call that one.

[00:05:58]Clear? If 100% is one and we want to find the value of 50%. What is the value of 50%? 1 by half of the total value, which is 50 by 100 or 1 by 2.

[00:06:11]Clear? The first thing what you should know that what is the equivalent fractional value? Equivalent fractional value to any percentage things. Fine.

[00:06:21]So, the first thing we'll be learning today is how to convert percentage in the form of mixed fraction. How to convert percentage in the form of how much?

[00:06:32]Mixed fraction. How will we do this?

[00:06:34]Suppose we have the value of 205%.

[00:06:39]205%.

[00:06:40]I need to convert this in the form of fractions.

[00:06:43]Right? So, 205% there are two ways to do. One thing I can write 205% is 205 divided by 100. If you'll cancel by five, this is 41 by 20.

[00:06:59]What is another approach to do so?

[00:07:03]205% also I can write as 200% plus 5%.

[00:07:12]What is value of 200%? You know that 100% is one. So, the value of 200% will be equal to two. What is the value of 5%? 5% is 5 by 100 or 1 by 20.

[00:07:27]So, what is the answer then? 20 into two, 40. 40 plus one, 41 by 20. Now, you may ask me one thing.

[00:07:34]Sir, you know this directly we can write 205% in the form of 40 by 20.

[00:07:40]Right? Then why we are doing this approach? 205% as 200% plus 5%.

[00:07:47]So, if the number is given as a proper number, this is easier to do. We can do that. But sometimes, you will see that numbers will come in the form of decimal numbers also.

[00:07:58]In that case, if you won't adopt this approach of solving, it will be tough to convert in the form of how much?

[00:08:05]Fraction.

[00:08:07]Right.

[00:08:09]Fine.

[00:08:11]Then, so there are two approach. One we can do either by this approach or we can apply which one? This approach. Next, how do we find 225%?

[00:08:24]Similarly, 225% we can say 200% which is two.

[00:08:30]Plus, what is next value? 25%. What is the value of 25%? 25 by 100, which is 1 by 4. 4 into two, eight. 8 plus one, 9 by 4.

[00:08:43]Right? So, we are trying to adopt which process? The process of writing fraction the process of writing how much?

[00:08:49]Percentage in the form of fractions, but in this approach, not writing 225 by 100 part.

[00:08:56]Right? Next one. Suppose we have to find the value of 508%.

[00:09:00]How will we do this?

[00:09:04]What is the value of 500%? 100% is one.

[00:09:08]So, the value of 500% will be equal to five. Plus, what is second value? 8%.

[00:09:14]What is value of 8%?

[00:09:17]8 by 100.

[00:09:20]Or we can say 4 * 2 = 8, 25. 25 * 5, 125 + 2, 127 by 25. This is how we convert what?

[00:09:32]Percentage in the form of which one?

[00:09:34]Fraction.

[00:09:35]How do we write this one then? 337.5%.

[00:09:40]Right? So, now we can say 337.5% will be equal to that. If I'm looking from the first approach, what is the answer?

[00:09:51]This value will be equal to 337.5 divided by 100. Cancel Cancellation is not going to be easier. Another approach is I can write 337.5% as 300% + 37.5%.

[00:10:11]Clear? Now, I'll tell you suppose if the answers are given in the form of which one decimal value, how to write in the form of fractional things, right? First, go through that part.

[00:10:23]Just think of this.

[00:10:25]So, suppose Now, we know that 1 is how much? 100%.

[00:10:35]1 is 100%. What is the value of 1/2?

[00:10:39]Just now we discussed 1/2 will be equal to 50%.

[00:10:43]If you know the value of 1/2, I think we can also directly solve find the value of 1/4. What is the value of 1/4? Half of 1/2, which is 25%.

[00:10:55]Clear? Then, 1/4 is 25%. What is the value of 1/8? 1/8 is half of 25, which is 12.5%.

[00:11:05]1/8.

[00:11:07]What is the value of 1/16? Half of 1/8.

[00:11:11]12 8 is half is 6. Half of 0.5 is 0.25%.

[00:11:17]Clear? Then, in the exam, we don't have time to what multiply by 100 and find the answer.

[00:11:24]Actually, basic approach is how much?

[00:11:25]Any value multiply by 100 and find convert in the form of percentage. You don't have this much of time to do in the exam. So, what we do basically, we'll practice this fraction to ratio part. Fraction to percentage. If you can remember, the problem solving will be more easier for us.

[00:11:45]Clear? Then, second part is So, we did everything in the form of how much? 1/2, 1/4, 1/8, 1/16. Suppose we have What is the value of then 1/3?

[00:11:58]If you multiply by 100 and convert in the form of percentage, this value will be 33.33%.

[00:12:07]Or we can say 33 1/3% Then, the 1/3 is done. 1/4 already we have covered. What is the value of 1/5?

[00:12:23]This is simple. 1/5 will be equal to in the form of percentage 20%.

[00:12:29]Clear? Then, third value.

[00:12:32]Now, two ratios which are very simple to remember. One is 1/9 and fourth one is 1/11.

[00:12:43]What is the value of 1/9 in percentage?

[00:12:45]If you convert this in the form of percentage, the value of 1/9 will be equal to 11 1/9.

[00:12:56]1/11 value is 9 1/11.

[00:13:03]Easy to remember. What is fraction 1/9?

[00:13:06]11 1/9%. The value of 1/11 is 9 1/11%.

[00:13:12]Fine. Then, 1/9 even if you're dividing, the answer will be in the form of 0.11. So, this is 11.11%.

[00:13:21]1/11 in the form of decimal will be 9.09%.

[00:13:29]Clear? Now, why we are doing all this?

[00:13:31]Sometimes, they'll ask you find 11.11% of Just take one example. Find the value of Find 11.11% of 2200 Oh, sorry, let me call 7200.

[00:13:50]If you know directly value of 11.11% in the form of fraction, the problem solving will be very easy. How will I do this? 11.11% is nothing but 1/9. 1/9 of 7200.

[00:14:04]What is the answer? 9 8 are 72. This answer will be 800.

[00:14:10]If you don't know how to this value level 11.11% is 1/9, then we have to solve it and that solving takes a lot of time again.

[00:14:19]Clear? What are the things you have you have to learn? 1/2, 1/4, 1/8, 1/16.

[00:14:25]1/3, 1/5 always we are in practice with this. 1/9 and 1/11 part also you have to be careful. Then, other than that, what we need to know extra part?

[00:14:37]Just wait.

[00:14:40]What value of 1/7?

[00:14:43]Easy to remember this one. 1/7 in the form of percentage is 14.28%.

[00:14:50]How will you remember this?

[00:14:53]7 into 2 14. 14 into 2 28. Just a simple observation. 14.28% also we can write 14 2/7%.

[00:15:04]The value of 1/7.

[00:15:06]Then, 1/6 and 1/15 as a pair you can remember. Let me call this is fourth one. This one is fifth one.

[00:15:17]1/6 is 16.66%.

[00:15:22]Or 16.

[00:15:25]2 16 2/3% in the form of fractions.

[00:15:31]Clear? What is the value of 1/5? 1/5 in the form of percentage is 6 2/3%.

[00:15:40]Clear? You can remember like 1 + 5 is 6.

[00:15:42]Just a shortcut to do that. 6 2/3% or we can say 6.66%.

[00:15:50]The 1/6 is 16.66%.

[00:15:54]1/15 is 6.66% fraction in the form of percentage.

[00:15:59]Right? Moving next one.

[00:16:01]Seventh one is also if you can remember the value of 1/12, which is 8.13%.

[00:16:09]8 of 1/3% or 8.33%.

[00:16:16]Don't expect to be excellent in all these things in one day. Just by practice repeatedly, we can be excellent in these topics. Fine. So, So, what we are basically we are doing? We are converting a fraction in the form of percentage. The process is simple, but what I'm telling you if you could remember some of the fraction to percentage, it is easier for us to solve a good problem. It will save our time.

[00:16:41]The process is how much? Whenever we have a fraction, for example, 1/2, if you multiply the fraction by 100, it will be converted in the form of percentage. Right? But we don't have enough time to do this process again and again in the problem exam.

[00:16:56]Clear? Then, Now, why we are doing all this? Suppose they are asking you to find the value of Find 8 1/3% of Uh let me say we have 1200 84.

[00:17:27]8 1/3% of 1284. If you are in practice, we know that 8 1/3% is nothing but in the form of fractions 1/12. So, what is the value of 1/12 of 1284?

[00:17:41]12 ones are 12.

[00:17:42]0 12 sevens are 84. So, 8 1/3% of 1284 will be equal to 107. One more thing, take as a note point.

[00:18:01]We know that what is the value of 1/4?

[00:18:06]25%.

[00:18:08]If the value of 1/4 is 25%, then what is the value of 3/4? This series we should know that. 3/4 will be 3 into 25, which is 75%.

[00:18:20]Fine. What is the value of 1/8?

[00:18:25]Look for the 1/8 series.

[00:18:27]1/8 is nothing but half of 1/4. 1/4 is 25%, so 1/8 will be equal to 12.5%.

[00:18:38]Right? This series is also very important in solving problem. If you know the value of 1/8, then what is the value of 3/8?

[00:18:46]Multiply by 3 in this. If you multiply 12.5 into 3, the answer will be equal to 37.5%.

[00:18:56]Clear? So, the value of 3/8 will be equal to 37.5%.

[00:19:01]Then, what is the value of 7/8?

[00:19:06]Multiply this one. This value will be 87.5%.

[00:19:12]And the value of 5/8 will be equal to 62.5%.

[00:19:20]Clear? So, two series which are very important. One First one is how much?

[00:19:24]1/4. We are always habituated 1/4 is 25%. The value of 3/4 will be equal to 75%. Similarly, the value of 1/8 series is important. 1/8 is 12.5, 3/8 37.5, 5/8. Even if you don't know all this, if you just remember 1/8, at that time we can guess with this value. 0.5 0.5 0.5 whenever is coming, denominator must be what in the form of 1 by 8 pattern.

[00:19:54]Clear? Slightly guess here and there can make your problem will be easier to solve it. Clear? Then.

[00:20:01]Just practice one thing. Suppose what 16.66%?

[00:20:06]What is the fractional value of this?

[00:20:10]Take a pause. Think. One is 16.66% and other is 6.66% percent. We have to deal again and again with this concept. 16.66% is nothing but which value?

[00:20:23]1 by 8.

[00:20:27]1 by how much? 8. 1 by 8 or 1 by 16? 1 by 6.

[00:20:32]And the value of 66.66% is 1 by 15.

[00:20:37]Clear? We have to repeatedly use this concept in solving the problem. Now moving to this part.

[00:20:47]So earlier we are finding the value of how much? 337.5% and we are converting this in the form of which one? In the form of P by Q or in the form of a fraction.

[00:20:59]Right? So suppose we have 337.5%.

[00:21:03]How will I write this in the form of P by Q or in the form of fractions?

[00:21:08]This we can write as 300% plus 37.5%.

[00:21:15]What is the value of 300% as a number?

[00:21:17]This is three plus 37.5% is the value of 3 by 8.

[00:21:24]If you will calculate what is the answer? 8 * 3 = 24. 24 + 3 27 by 8.

[00:21:31]I hope all of you are clear with this.

[00:21:34]Yes.

[00:21:37]Yeah.

[00:21:38]>> [snorts] >> Let's move to the next slide.

[00:21:44]>> [snorts] >> Let's try this one.

[00:21:50]We have to find the value of 366.66% in the form of P by Q. Directly dividing by 100 if you will do and then cancellation will take a lot of time so we'll break this one in the form of Yeah.

[00:22:08]Think of it. First part is very clear.

[00:22:10]300. 300 we can write in the form of fractions. Fractional value is three plus what is left next? 66.66% Any guesses from all of you?

[00:22:20]66.66% will be how much?

[00:22:25]Right?

[00:22:28]Yeah. Think of this. What is the value of 66.66%?

[00:22:31]If you remember this 1 by 3 you can guess like that. 1 by 3 is 33.33%.

[00:22:40]Clear? Then what is the value of 66.66%?

[00:22:43]This is the value of 2 by 3. If you will calculate what is the answer? 9 + 2 11 by 3.

[00:22:51]Moving to the next one. 387.5.

[00:22:55]387 means 300 which which is three plus 300% will be equal to three plus 87.5%.

[00:23:05]Right? Again 1 by 8 series.

[00:23:09]1 by 8 is 12.5.

[00:23:14]Right? If you will multiply by seven this is 87.5.

[00:23:18]So 3 + 7 by 8. 8 * 3 24. 24 + 7 31 by 8.

[00:23:27]Then. What is the value of 488.89%?

[00:23:32]Can I say that this is nothing but 500% minus if this number is close to 500. So 500% minus 11.11%?

[00:23:49]Clear? Then.

[00:23:50]The 500% in the form of fractions we can say 5 by 1 minus what is 11.11%?

[00:23:59]Two values you have to keep repeatedly have to remember. One is 1 by 9 and other is 1 by 11.

[00:24:06]What is 1 by 9? 11.11.

[00:24:10]1 by 11 is 9.09%.

[00:24:17]Clear? So 5 11.11 is nothing but 1 by 9.

[00:24:21]What is the answer? 45 minus 1 44 by 9.

[00:24:26]Similarly we have to find the value of 583.33% Any guesses how to do this?

[00:24:35]Can I write this as 600% which is this number is close to 600 minus 16.66%?

[00:24:45]What is 600%? This is six minus 16.66% the value of 1 by 6.

[00:24:55]So 36 minus 1 35 by 6. If you just keep divide by 100 and cancel it will take a lot of time to do these problems. Fine.

[00:25:04]So we're moving to the next problem next slide.

[00:25:07]341.66.

[00:25:09]Anyone any guesses how to do this?

[00:25:12]Think of this. How to find 341.66%?

[00:25:16]We have to convert this in the form of P by Q. How will you break this one?

[00:25:23]Yeah.

[00:25:25]Any guesses how to do this?

[00:25:28]First thing is 300% we are very clear.

[00:25:31]300% value of 300% is three plus what is left now? 41.66.

[00:25:37]I think 25 plus 16.66%?

[00:25:46]3 plus the value of 25% is 1 by 4 plus the value of 16.66% is 1 by 6. What is LCM?

[00:25:57]4 and 6 LCM will be equal to 12.

[00:26:01]So 36 plus 3 plus 2.

[00:26:06]What is the answer? 36 plus 5. 41 by 12.

[00:26:15]Clear? Then. 716.66.

[00:26:19]Easily this can be you can guess it.

[00:26:21]700% is seven plus 16.66% is 1 by 6 which is 43 divided by 6.

[00:26:32]787.5.

[00:26:35]700 7 plus 87.5 is 7 by 8.

[00:26:42]856. 56 plus 7 63.

[00:26:49]56 plus 7 how much? 63 divided by 8. Right.

[00:26:55]>> [snorts] >> Move to the next slide. Then. So now you have learned how to convert percentage in the form of fraction. Now we are trying to learn convert which one? Fraction in the form of percentage.

[00:27:09]Fraction in the form of percentage. Then to approach the first one you know that how to convert fraction in the form of percentage we'll multiply by 100.

[00:27:19]Multiply by how much? 100 to convert the fraction in the form of percentage. What is the answer? This will be 700 by 3.

[00:27:26]Again we have to divide and find the answer in the form of decimal. We'll look for the alternative approach.

[00:27:32]Clear? What is 7 by 3 if I will break this one?

[00:27:36]Can I say this value is 7 we can think as 6 plus 1 by 3?

[00:27:43]I hope it is clear to all of you.

[00:27:46]7 by 3 6 plus 1 by 3. 6 why we are writing the form of six? The closest multiple of three which is close to seven.

[00:27:54]Right? The multiple of three which is closest multiple of three which is close to seven. 6 by 3. 6 by 3 will be equal to 2. So this is 2 plus 1 by 3.

[00:28:07]I hope all of you must be clear.

[00:28:09]Right? Now I have to convert this in the form of how much percentage? Two in the form of percentage is 200%.

[00:28:17]Plus 1 by 3 in the form of percentage is 33.33%.

[00:28:23]So what is the final answer? This will be equal to 233.33%.

[00:28:29]Just have a practice habit. If you will practice regularly you can easily solve this problem by converting fraction in the form of I call mixed fraction and then solve the problem.

[00:28:40]Clear? Then. What is 17 by 4? How will I write this? 17 by 4 can I write in the form of 16 plus 1 by 4 or 4 plus 1 by 4?

[00:28:52]4 is nothing but in the form of percentage 400% plus 1 by 4 is 25% which is 425%.

[00:29:02]Similarly 23 by 6. So 23 we can think as 24 minus 1 because the closest multiple of 6. Multiple of 6 which is very close to 23 is 24. So 24 minus 1 by 6 or we can write 6 minus 1 by 6.

[00:29:23]What is 6? 6 in the form of percentage is 600% minus 1 by 6 is 16.66%.

[00:29:35]What is the answer? 600 minus 16.

[00:29:40]584. So 583.66.

[00:29:46]0.33.

[00:29:52]percent 583.33% then 26 by 5 how will I do 26 by 5? Can I write this as 5 + 1 by 5?

[00:30:04]5 is how much? 500% + 1 by 5 will be in the form of 20% which will be equal to 520%.

[00:30:15]Other question in the similar fashion you will do that. I hope you are clear.

[00:30:19]So without multiplying by 100 we are trying to convert a fraction in the form of mixed fraction and then finding converting in the form of percentage.

[00:30:28]The actual What is the your conventional approach? We are multiplying by 100 and then dividing which will take a lot of time so we'll cut how much we'll take this process to solve it.

[00:30:38]Right. Let's move to the next concept.

[00:30:41]>> [snorts] >> Then.

[00:30:43]Now one thing is first thing when we turn talk about percentage we have to learn the first concept is A percent of B will always be equal to B percent of A. What is meaning of A percent of B? A percent means A by 100 into B. B by 100 into A. In both the cases your answer is how much? AB by 100. Clear? So A percent of B you say or B percent of A you say your answer will always be equal. Then what is use of this concept? Now for example we have to find the value of 120% of 37.5.

[00:31:20]Clear? Now if when you see 37.5 one thing should strike in your mind. What is 37.5?

[00:31:27]If we'll I'll convert this in the form of percentage what is 37.5?

[00:31:32]1 by 8. What is 1 by 8? 12.5.

[00:31:36]1 by 8 is 12.5%.

[00:31:39]3 by 8 is 37.5%.

[00:31:45]Right? Since A percent of B is equal to B percent of A this also we can write as 37.5% of 120.

[00:31:56]Writing A percent of B in the form of B percent of A.

[00:32:00]Then how will we do this?

[00:32:02]37.5% we can write in the form of fraction is 3 by 8 into 120.

[00:32:10]4 into 2 4 into 3 30 2 into 15 so 15 into 3 will be equal to 45.

[00:32:21]I'll just have a look.

[00:32:23]6 minus 1 by 6 is 5 by 6 600.

[00:32:30]Correct or not?

[00:32:31]>> [clears throat] >> I'm sorry.

[00:32:36]600 minus 16 Yeah.

[00:32:43]>> [snorts] >> Thank you.

[00:32:46]Now we have to find the value of 45% of 350. How will we do this?

[00:32:54]How will you find 45% of 350? The first thing is again I don't want to go with finding 45% of a number. One thing is I think all of you are sure about how to find 50% of a number. What is 50% of a number? So 45% also I can write in the form of 50% minus 5%.

[00:33:13]Of how much? 350.

[00:33:16]What is 50%? 50% is 1 by 2.

[00:33:21]So let's find 50% of 350. So 1 by 2 of 350 175.

[00:33:27]Minus what is value of 5%? Then we know that for 350 we have any number is given. For example the number is given in the form of let's say 800.

[00:33:41]Clear? If I ask you to this number is itself is how much? 100%.

[00:33:46]If I ask you to find 10% of this number how will you do this?

[00:33:50]So 10% will be equal to 1 by 10 of this number. So the answer will be equal to 1 by 10 of 800 is 80 or put decimal one after one place from the right side. Right? Next part.

[00:34:04]This is value of how much? 10%.

[00:34:07]If I ask you to find 1% of this number.

[00:34:09]1% of which one? 800.

[00:34:12]Put decimal after two places answer will be equal to eight. Then what is the value of 5% of this number?

[00:34:19]Since the value of 1% is eight the value of 5% will be equal to 8 into 5 which is 40.

[00:34:27]Clear? Then so what we are finding? 45% so we have to find 50% minus 5%. What is 50%? 50% is nothing but half of this number which is 175. Now we have to find 5% of the given number. What is 5%? That is half of 10%. What is 10% here? 35. What is 10%? 35. Then half will be equal to 17.5.

[00:34:52]Subtract this one.

[00:34:55]175 minus 18 do that and add 0.5. What is 175 minus 18?

[00:35:04]15 163 will be 157 so this is 157.5.

[00:35:12]Once check it. 157 158 plus 7 175. Fine. Then we have to find 76.66% of 30. Guess it. How will you do this?

[00:35:25]76.66% of 30.

[00:35:35]23 by 6 4 minus 1 by 6 right?

[00:35:38]Yeah.

[00:35:39]Yeah there was a small error here. 20 There was small error. 23 by 6 if you'll convert it 24 minus 1 so it is 4 minus 1 by 6 which is 400 minus 16.66.

[00:35:53]So the value will be equal to 383.33%.

[00:36:01]I hope you understood the concept how we are doing that. This is 24 minus 1 by 6.

[00:36:07]Fine.

[00:36:10]Then how will you find 76.66% of 30?

[00:36:15]76.66% can I write this in the form of any guess how will you do? 60% is easier to find out. 16.66% we know how to do that. What is 60%? So I'll write this in the form of 60% plus 16.66% of 30 we have to find out.

[00:36:37]Clear? Then what is 60% of this number?

[00:36:41]We know that 10% is three. 10% is how much? Three. So 60% will be equal to 18.

[00:36:49]Plus what is 16.66%?

[00:36:52]1 by 6 of 30. 1 by 6 of 30 is 5. So 18 plus 5 is 23. Simple to solve this one.

[00:37:00]You don't have to calculate all this value. Next. 14.28%.

[00:37:05]What is 14.28? If you remember this in the form of fractions. 14.28 is nothing but 1 by 7 in the form of fractions into 3750.

[00:37:19]7 5 are 35. What is left then? 3725.

[00:37:25]7 3 are 21.

[00:37:28]40 40 means 7 5 are 35.

[00:37:34]So 535.

[00:37:36]50 so 50 will be something 535.7.

[00:37:41]Let's check once. 7 5 are 35 25 7 3 are 21 40 7 5 are 35.

[00:37:49]50 7 7 are 49. So 535.7 approximate value of 14.28% of 3750.

[00:37:58]I hope you understood this concept. So what we are trying to do? We are not taking the conventional approach to solve the problem. We are breaking the percentage in the form of how much? 10% 5% and so on and then we are solving a problem. Let's try few more problems.

[00:38:15]Suppose if I ask you to find the value of find 49% of find 49% of let's see a number 320.

[00:38:32]How will you do this?

[00:38:33]Right? Can I say 49% is very close to 50%?

[00:38:38]Why I'm taking 50%? Because we know how to simply find the 50% of this number.

[00:38:43]50% of this number. So I'll call this as 50% minus 1% of 320.

[00:38:53]Clear? 50% is how much? 1 by 2. 1 by 2 of 320 how much? 160. Minus 1%. What is value of 1%?

[00:39:05]3.2. 10% is 32. 1% is 3.2.

[00:39:11]Right? So what is answer? 156.

[00:39:16]Point eight.

[00:39:20]Clear? So 49% of 320 will be equal to 156.8.

[00:39:25]Try one more example. Suppose we have to find find the value of let me see 33.33% of 340.

[00:39:45]5 What is 33.33%?

[00:39:49]1/3. So, we have to find 1/3 of 341.

[00:39:55]115 >> [clears throat] >> Fine.

[00:40:00]Try one more problem. Suppose you have to find the value of 58% of 800 Clear? 50% is how much? 400 Plus what is the value of 8%? 1% is 8.

[00:40:23]So, 8% will be 1% is 8. So, what is the value of 8%? 8 into 8 64. So, the answer will be equal to 464.

[00:40:32]That's all. I hope you are clear with how to convert percentage in the form of fractions and fraction in the form of percentage. One more thing I'll tell to all of you. Unless you practice this type of things again and again, you'll not be perfect in that. So, try to solve how much? Create your own problems and try to solve at least 20 to 30 more problems. How to convert percentage in the form of fractions and fraction in the form of percentage to get excellent in your examinations. Right? Then. Now, on the basis of percentage, we'll try to solve few more problems which are being asked in the competitive exams. Right?

[00:41:07]So, let's see these problems.

[00:41:29]Right.

[00:41:38]What is given?

[00:41:39]When a number is increased by 216 it becomes 140% of itself.

[00:41:46]When a number is increased by how much?

[00:41:48]206 216. It is it becomes 140% of itself. What is the number?

[00:41:54]I'm just trying to just solve this problem by two different approach. One is the conventional approach and one is we'll apply the shortcut. And then, we'll apply those those shortcut method for all other problems. Right? What is the conventional approach?

[00:42:07]We'll call the number is equal to how much? X. What is X here? If the number is X when X is increased by how much? 216, it becomes 140% of the number, which is 140% of X.

[00:42:22]This is what the basic statement from the statement we can see.

[00:42:26]Fine. So, X plus 216 will be equal to What is the value of 140% of X? It is 140 by 100 or 14 by 10 X.

[00:42:42]Clear? So, 216 will be equal to 7 by 10 X minus X or the value of 216 is Is 7 by 10 or 7 by 5? We'll cancel by 2.

[00:43:00]7 by 5 X minus X. Fine.

[00:43:04]Which is 216 equal to 7 X minus 5 X 2 X by 5. Therefore, the value of X will be equal to 216 multiplied by 5 divided by 2, which is 108 into 5.

[00:43:22]How much? 540 So, the value of X must be equal to 540.

[00:43:28]This is what we get the conventional approach to solve the problem. Right?

[00:43:32]What are different approach we can do in this problem? In the earlier classes, I told you if you remember this part.

[00:43:37]If I write 25% For example, I'm writing 25% as 1 by 4. What is the meaning of this?

[00:43:45]If I'll take the number as 4 then it's 25% is 1.

[00:43:51]What is 25%? If I take the number as 4, then it's 25% is how much? 1. What is given here?

[00:44:03]Right. When a number is increased by 216, it becomes 140% of itself. What is 140%? Think on this.

[00:44:12]140% is 140 by 100, which is nothing but 7 by 5.

[00:44:18]Right? So, can I say that if my number is 5 then it's 140% will be equal to 7.

[00:44:25]If the number is 5, it's 140% is how much? 7. So, I'll call my original number as 5.

[00:44:34]Original number I'm calling as how much?

[00:44:36]5 or let me call it 5 part. Then after increment of 41 40%, this number will be equal to how much? The new number is 7.

[00:44:51]If the original number is 5, then it's 140% is how much? 7.

[00:44:56]I hope you are clear with this. What is the difference between these two number?

[00:44:59]New number to original number, that is two part.

[00:45:03]Clear? Let me call this original number as some 5 part.

[00:45:06]This is 7 part.

[00:45:08]What is the difference? Do you know the difference is nothing but two part.

[00:45:13]Clear? When the number is increased by 140% of itself, the increase is how much? 216. Hence, we can say my two part is 216.

[00:45:23]The increment is how much? 216. So, two part is 216. Therefore, the value of one part will be equal to 108.

[00:45:32]What we have to find? We have to find the original number. What is original number? The original number is 5 part, which is 5 into 108.

[00:45:41]Which is 540.

[00:45:43]A simple approach. Right? This only you'll get it by practicing again and again. Only with the help of percentage, we can directly see this problem.

[00:45:51]Clear? We don't have to solve again and again. 140% is 7 by 5. Original part is 5 part. After increment, it is 7 part.

[00:45:58]What is the difference? Two part. Two part is given as how much? 216. What is the value of one part? 108. What is the new original number? 5 part. So, 5 into 108, which is 540. Simple.

[00:46:08]Clear? Let's try few more problems based on the similar concept.

[00:46:14]6 2 by 3% of a number is subtracted from itself, then result becomes 5670.

[00:46:22]Clear? If you have the idea about 6 2 by 3%, directly we can see this problem.

[00:46:28]What is 6 2 by 3%? Two values I asked you to remember. One is 1 by 6 and 1 by 15. As a pair, remember these two values. Easy to remember this. 1 by 6 is 16.66% and 1 by 5 is 6.66%.

[00:46:46]Then.

[00:46:47]6 6.66% or 6 2 by 3%.

[00:46:54]In the form of fractions, 6 2 by 3% is nothing but 1 by 5.

[00:46:59]1 by 15 Clear? Then. So, what is my original number? 15 part.

[00:47:06]New number is how much? One part. So, this is original number is and this is new number.

[00:47:18]15 part, this is new number is one part.

[00:47:24]What is given here?

[00:47:27]6 2 by 3% of a number and you know that if the number is 15, then it's 6 2 by 3% will be equal to 1. Right? If 6 2 by 3% of a number is subtracted from itself, means 15 part is original. If one part is subtracted, then what is left? 14 part is left.

[00:47:46]Subtracted from itself, then result becomes 5670.

[00:47:50]This is 5670.

[00:47:53]That's all.

[00:47:54]Original part minus new part, which is subtracted, the answer is 5670.

[00:48:00]So, the value of one part will be equal to 14 4's are 56. 0 14 5's are 70. So, what is the value of one part? 405. What they're asking you to solve it? We have to find the original number. What is original number? 15 part.

[00:48:17]Original number is 15 part. So, the value of 15 part will be equal to 15 into 405.

[00:48:29]What is answer?

[00:48:30]400 into 15 6000 75 Clear?

[00:48:43]Fine. So, what is original number? 15 part. Again, look carefully what I said.

[00:48:47]If you write 1 by 15 here, what is when 1 by 15? 1 by 15 is 6 2 by 3%. What is 1 by 15? 6 2 by 3%. If the number is 15, then it's 6 2 by 3% will be equal to 1.

[00:49:01]That's all. Simple idea of this.

[00:49:03]Right. Moving to the next problem.

[00:49:07]Then.

[00:49:08]First one. So, very simple. You must be knowing all this.

[00:49:12]Just just observe the pattern here. 85 is what percent of 510? 85 is what percent of 510? How will I solve this?

[00:49:21]85 What percent of 510 is 85 by 510 into 100?

[00:49:32]Clear? What is 85 by 510 into 100? Zero cancel out.

[00:49:37]17 threes are 17 into five 85.

[00:49:41]So the answer will be equal to 1050 by three.

[00:49:48]What is 50 by three? 16 threes are 48.

[00:49:52]16 two by three percent.

[00:49:55]16 three threes are 48 two by three percent. Clear? So whenever they say how much 85 is what percentage is of 512? So whatever is connected with of put in the form of denominator.

[00:50:07]Clear? Or in the simple sense what exactly they are saying? Suppose the number is 510.

[00:50:13]What is its 10%?

[00:50:16]10% of this number is how much? 51.

[00:50:19]Clear? Your answer is how much 85. It must be more than 10%. What is the 5% of this number?

[00:50:27]Half of 51. Half of 51 will be 25.5.

[00:50:32]Still it is more. So I can see that the answer will be what? Approximately more than how much? 15% which is coming in the form of 16 two by three percent.

[00:50:40]Clear? So basically what they are trying, they are asking you find different percentage of 510. And this 85 becomes how much percent of 510? Right.

[00:50:50]Moving to the next one. 150 is what percent less than 400? 150 is what percent less than 400? Right? First thing is whenever this type of problem is given, first forget about percentage.

[00:51:04]150 is how much more than 400? Find out.

[00:51:08]So we know that 150 250 less than 400.

[00:51:14]Clear? 250 and we are comparing with which number? The basic number which is 400. So 250 by 400 into 100.

[00:51:24]Cancel out here.

[00:51:26]So what is left here? 250 by four. Or we can say 125 by two percent.

[00:51:33]What is 120 by two percent? This is 62.5%.

[00:51:40]Right. Next. 840 is what percent more than 260? So we are comparing with which one? 260. First thing is what we are supposed to find? 840 is how much more than 260? Then we'll convert this in the form of percentage. So 840 minus 260 find out.

[00:51:59]840 minus 260. That is what the difference. This value comparing with how much? 260 multiplied by 100.

[00:52:09]Right? So can I say that whenever we have to find more or less, which what we are doing the concept? Find the difference.

[00:52:17]Find which one? Difference divided by the base value. Base value means the original value. Multiplied by 100.

[00:52:26]For which one? Either more or less percentage.

[00:52:29]I hope you must be clear with this.

[00:52:31]Again, you need to practice this model for at least two three problems to be get perfect in that.

[00:52:37]That's simple.

[00:52:38]What is next one?

[00:52:40]P is six times of Q.

[00:52:44]Just wait a minute.

[00:53:25]Yeah. Just see once.

[00:53:30]Four four of three.

[00:53:33]It was three earlier only. So I'll make it four five.

[00:53:40]Now what is given?

[00:53:41]P is six times of Q. Then Q is what percentage less than P?

[00:53:47]Again this is very simple.

[00:53:49]When I say right P is six times of Q, what mathematical statement can we make?

[00:53:54]Can I say that the value of P will be equal to six Q. That is P is how much? Six times of Q.

[00:54:02]Then or the ratio of P by Q must be equal to six is to one.

[00:54:11]I hope you are clear with this.

[00:54:13]Q is what percentage less than P? So we are comparing is how much? With P.

[00:54:19]Clear? What percent less or more what I'll do? We'll subtract both the values.

[00:54:24]So difference.

[00:54:27]Difference divided by base value. Base value means the value what we compare with. So we are comparing with which one? P. P is how much? Six. Into 100.

[00:54:40]What is difference here? Six and one difference is five by six multiplied by how much? 100.

[00:54:49]Clear? What is five by six by 100?

[00:54:54]500 by six.

[00:55:00]How much?

[00:55:02]Six eights are 48.

[00:55:04]20. Six threes are 18.

[00:55:09]20.

[00:55:11]83.33%.

[00:55:15]83. How much? 33%.

[00:55:18]So what we can say? The Q is less than P by how much? 83.33%.

[00:55:24]The idea was how much simple? We are writing P in the form of six Q or the ratio of P by Q will be six by one.

[00:55:31]Comparing how much? Q is what percent less than P? First thing what we are finding, Q is how much less than P? So Q is five less than P. That difference divided by we are comparing with P. So by six into 100. Which is 83.33%.

[00:55:49]Hope you are clear with this.

[00:55:51]Second. Moving to the seventh one. If A is 20% more than B, then B is what percent less than A?

[00:56:03]Now again take the meaning of 20%. What is the meaning of 20%? 20% is nothing but one by five.

[00:56:11]Clear? Then A is 20% more than B. So if I'll take the value of B as five part.

[00:56:20]A is 20% more than B. And 20% of five is one. So the value of A must be equal to six.

[00:56:28]So if B is five part, the value of A must be equal to how much? Six part.

[00:56:33]Then what they have we are comparing? B is what percent less than A? First thing is B is how much less than A? B is one less than A. So one divided by we are comparing with how much? A. So one by six into 100.

[00:56:49]And we know that one by six is nothing but 16.66%.

[00:56:56]I hope you are clear with this. So the whenever they ask you how much, how much less than or how much more than, find the difference divided by which one?

[00:57:05]Base quantity multiplied by 100.

[00:57:08]Clear? So we have done how much? At least we have done 10 12 problems.

[00:57:13]Of this I think all of you understood.

[00:57:16]Yes.

[00:57:20]Any comment? Anyone? Am I very fast?

[00:57:26]Or I have to go with the same pace if you are able to understand it.

[00:57:33]You can write in the chat box.

[00:57:43]Yeah.

[00:57:44]Fine.

[00:57:45]So let's move to the next problem.

[00:57:51]A student gets 250 marks and yet failed by 38 marks.

[00:57:57]Right? So what he is saying? Student is getting 250 marks but failed by 38 marks. If 40% is the passing marks, then what is the maximum mark? What is the passing mark? Passing mark here? 40%. So what is given here?

[00:58:12]Student is getting 250 marks.

[00:58:15]If he'll get 38 more marks, can I say that he will pass in the exam? He is failing by 38 marks means if he'll get 38 more marks, he will pass in the exam.

[00:58:24]That is 40% of the passing mark.

[00:58:28]What is 40 passing mark?

[00:58:30]40%.

[00:58:34]Right? So if he get 250 marks plus 38 more marks, he will get the passing mark and that is given as 40%. So I can see that the value of 40% will be equal to 250 plus 38, which is 288.

[00:58:50]If the value of 40% is 288, what is the maximum mark in the exam? It means we have to find the value of 100%. How will I do this?

[00:59:00]If the value of 40% is 288, how will you find the value of 100%? Can I say 100% I can break like that? 40% plus 40% plus 20% I'm writing in the form of 40%.

[00:59:15]What is 40%? 288.

[00:59:18]Again 40% what is answer? 288.

[00:59:22]20% is 144. Add up all this value. That is the total maximum mark in the exam.

[00:59:29]I hope all of you are clear with this.

[00:59:31]Right? Let's move to the one more problem.

[00:59:37]If a student score 36% of the mark, then he is failed by 32 marks. What is meaning of this?

[00:59:45]If you If he's getting 36% mark, he got failed by 32 marks. It means the passing marks is nothing but 36% plus 32.

[00:59:55]If you get 36% mark plus 32 marks, you will pass in the exam. But if he scored 48% mark, then he is passed by 64 marks.

[01:00:05]That means 48% marks minus 64 marks is nothing but the pass mark in the exam.

[01:00:13]What is the passing mark? It is either 36% plus 32 or 48% minus 64. If you will calculate this, what do we get it?

[01:00:23]36 if you will send this side, we'll get it 12%.

[01:00:27]Equal to 32 plus 64.

[01:00:32]4 plus 2 6, 6 plus 3 96.

[01:00:38]So, can I say 12% of the mark must be equal to 96?

[01:00:43]This is again passing mark.

[01:00:49]This value is also passing mark.

[01:00:52]I'm equating both the passing mark from the given equation.

[01:00:57]Right? If 12% is 96, what is the passing percentage we have to find out? Fine. If 12% is 96, what is the value of 1%?

[01:01:07]96 by 12, which is 8.

[01:01:10]1% is 8.

[01:01:12]Then, passing mark is nothing but either 36% plus 32 or 48% minus 64. Luckily, the number 32 is also multiple of 8.

[01:01:24]How much multiple of 8? If you will multiply by 4 here, 8 into 4 is 32. So, this value I can say 4%.

[01:01:32]So, what is the passing mark?

[01:01:34]Passing percentage mark will be equal to 36%.

[01:01:45]Plus 32% is nothing but 4%.

[01:01:49]So, the passing mark will be equal to 30 40%.

[01:01:55]You can check it in the second equation also.

[01:01:58]1% is 8. Then, what is the value of 64?

[01:02:02]64 will be equal to how much? 8%. 48 minus 8 40%. So, in any cases, we can say that the passing mark is nothing but 40%. That's what we are supposed to find. In the same problem, if they ask you, what is the find the maximum mark?

[01:02:17]How will I do this?

[01:02:20]You have to find the maximum mark in the examination. How will you do this?

[01:02:24]The value of 1% is 8. What is maximum mark? Maximum mark will be 100%. So, 100% will be equal to 800.

[01:02:33]So, maximum mark is 800 mark What is passing percentage mark, which is 40%? Suppose they ask you, what is the passing mark? How will I do this?

[01:02:44]Passing mark is in the form of percentage, which is 40%. The value of 1% is 32.

[01:02:50]Value of 1% is how much? 8. So, the value of 40% will be equal to 40 into 8, which is 320.

[01:03:00]Clear? So, these are the different problem they can ask here. Right? Let's move to the one more next problem.

[01:03:07]The radius of the circle is increased by 25%.

[01:03:11]Find the percentage change in its area.

[01:03:14]Clear? Again, let's solve solve this problem in two different approach.

[01:03:19]Right.

[01:03:21]If the radius of the circle is increased by 25%, what is the meaning of 25%?

[01:03:27]1 by 4.

[01:03:29]Clear? So, can I say that in the initially if the radius is 4, after increment of 1%, the radius will become 5.

[01:03:39]So, I'll call what this is original.

[01:03:46]And this is new one after increment.

[01:03:49]We are find how much we are comparing the change in area if the radius is changed by how much? Increased by 25%.

[01:03:57]This part is radius.

[01:03:59]When the initially radius is how much?

[01:04:01]4. Now, the radius becomes 5.

[01:04:06]Radius is how much? 4. Now, radius becomes 5, which is nothing but increment of 25%.

[01:04:12]Clear? Now, in this case, what is the area? Area will be pi r square, area of circle, which is pi into 4, which is 16 pi.

[01:04:20]What is area here?

[01:04:22]Pi r square, which is 25 pi.

[01:04:26]What we are asking you? Find the percentage change in the area. is the change in the area first we will find out.

[01:04:32]Change in the area is 9 pi.

[01:04:35]So, percentage change will be equal to change Change is nothing but 6 9 pi divided by how much? 16 pi into 100.

[01:04:48]Change divided by the what? The original value into 100.

[01:04:52]Then, one observation here. Can I say that the constant does not take part in this equation?

[01:04:58]Pi is anyhow is getting cancelled. You are finding the ratio. Whenever you will find the ratio, the constant part has no impact in the problem. So, whenever we solve such problems, like if you will do one more problem of the similar kind, I will not consider which part? The constant part in the problem. It has no use in solving how much? Finding the percentage change. Clear? So, what is the final answer? The percentage change will be equal to if I won't consider pi, directly we can say 25 minus 16 divided by 16 into 100.

[01:05:30]That's all. No need to consider which value? The value of pi.

[01:05:34]Which is 9 by 16 into 100.

[01:05:39]4 4 are 16. 4 25. 25 into 9 225 divided by 4.

[01:05:48]4 5 are 20.

[01:05:51]Then, what is 25? 4 6 are 24.

[01:05:55]1 by 4%. So, change in the area will be equal to how much? 56.

[01:06:00]56.25% or 56 1 by 4%. I hope you are all are clear. So, what is the output from this? One thing we can sure about whenever we have some constant in the problem and we are finding the percentage change, the constant has no impact in the problem. So, we can leave the constant in the upcoming problems.

[01:06:20]Right? Let's see one more similar problem.

[01:06:22]Now, the problem is based on rectangle.

[01:06:24]Earlier, we have what? One dimension where only radius was given. Now, we are talking about what? Length and breadth, both the things.

[01:06:32]If the length of the rectangle is increased by 37 and 1/2.

[01:06:36]Okay. So, first thing, what is the meaning of 37 and 1/2 degree?

[01:06:43]This is nothing but 3 by 8.

[01:06:46]20% is very simple. We know the value of 20% is 1 by 5.

[01:06:51]Clear? Now, see.

[01:06:53]If the length of the rectangle is increased by 37 and 1/2% and its breadth is decreased by 20%, find the percentage change in the area. Fine. So, we are finding what? Area in both the cases. I will say how much?

[01:07:08]Let me call this is length, this is breadth, and this one area.

[01:07:16]Clear? And then, this is original one.

[01:07:22]And after it's having changes, this is a new one.

[01:07:25]Right? What is the first thing?

[01:07:27]Length of the rectangle is increased by 37 and 1/2%. It means when the originally the area length is how much?

[01:07:34]8 unit.

[01:07:35]After the changes, it is increased by how much? 37 and 1/2. Means it is increased by 3. So, the breadth length will be equal to how much? New length will be equal to 11 unit.

[01:07:46]New length will be equal to how much? 11 unit. Then, breadth is decreased by 20%.

[01:07:51]Decrease by 20% means if the initial breadth is how much? 5.

[01:07:55]Initial breadth is how much? 5. It will decrease by how much? 1 unit. That is it becomes 4.

[01:08:02]Now, see what is the change in the area.

[01:08:04]In the first original area will be equal to 40.

[01:08:08]After this increment and this is decrease, now the area becomes 11 into 4, which is 44.

[01:08:14]What is the percentage change in the area? The percentage change will be equal to 44 minus 40, which is a change divided by the original area is how much? 40 into 100.

[01:08:29]Which is nothing but 10%.

[01:08:32]The percentage change in the area must be equal to how much? 10%.

[01:08:37]Clear?

[01:08:37]Simple things. If you have the idea about how much how to convert fraction in the form of percentage in the form of fractions, it becomes easier to solve the problems. What is 1 by 5? If the 5 is the original number, it's 20% is 1.

[01:08:51]If 8 is the original number, it's 37 and 1/2% is 3. Increment of 37 and 1/2% will be equal to 8 plus 3, which is 11.

[01:08:59]Decrease of 20% means 5 minus 1, which is 4.

[01:09:04]Very simple logic. Right? Move to the next one.

[01:09:08]So, you will try this by yourself. Just have a look here.

[01:09:11]If the base radius of a right circular cylinder is increased by 40%. 40% is simple. What is 40%?

[01:09:23]Is it 40 by 100? 40 by 100 is how much?

[01:09:26]2/5.

[01:09:30]Clear? What is 37.5 37 and 1/2? 3/8.

[01:09:40]What is given? Now, what is the volume of a cylinder? I think all of you must be knowing that volume of the cylinder is πr²h. π has no role to play in the problem because π is a constant value.

[01:09:52]Clear?

[01:09:53]Then, uh let me call it is depends on how much only? Radius and height. Let me call this is radius, this is height, this one is area.

[01:10:04]Clear? Then, initially, let me call this is original and this is new one.

[01:10:10]What is first thing?

[01:10:12]Radius is increased by 40% if the initial radius is five.

[01:10:19]Increase by 40% is 5 + 2, that is seven.

[01:10:23]Then, now, what is height? Height is decreased by 37 and 1/2%? That means if the initial height is eight, now the height becomes 8 - 3, which is five.

[01:10:35]I told you initially π will not take part in the problem. Let me write the formula is πr²h. π is constant, so just forget about the π part. r²h will be how much? 25 into eight, which is 200.

[01:10:51]In the second case, the area will be equal to 49 into 8 minus 49 into five.

[01:11:01]What is answer? 50 into five, 250. 250 minus five, 245.

[01:11:11]Fine. So, the original area is how much?

[01:11:14]200. New area is 245. What is the change?

[01:11:19]Change is 45.

[01:11:22]Change divided by the original area is how much? 200 multiplied by 100.

[01:11:28]What is answer we got it?

[01:11:31]200 is getting cancelled. 45 by two, which is 22.5% or 22 and 1/2%. The logic is very simple. I hope you can do any increment of any of these geometrical figure if one little thing is increasing or other thing is decreasing. How to find the percentage change in the what? The area or volume. Right? Let's move to a new type of problem.

[01:11:56]Now, the problems are based on income, expenditure, and saving. So, all of you know this one relation that income minus expenditure, this value will be equal to saving.

[01:12:16]Clear? A man has spent 75% of his income. So, I we don't know what is the income of the man, so let us assume that his income is how much? 100.

[01:12:28]Right?

[01:12:29]He has spent 75% of the income. So, expenditure, let me call 75% of the 100 is 75. So, his saving will be equal to 25.

[01:12:39]Then, if his income is increased by 20%. So, what is the initial income? 100.

[01:12:45]If it is increased by 20%, now the income will be equal to income new one.

[01:12:51]After increment of 20%, the new income will be equal to how much? 120.

[01:12:57]Clear? And if his expenditure is also increased by 10%, what is 10% of 75? 10% of 75 is 7.5. If we'll add this value will be 82.5.

[01:13:12]Value is how much? 82.5.

[01:13:15]Now, in this case, what is the value of saving?

[01:13:19]How much? 120. 120 minus 82 is how much?

[01:13:23]18.

[01:13:25]18 and then.5 17.5.

[01:13:30]Clear?

[01:13:32]>> [snorts] >> Oh, 17.5 plus 20, now?

[01:13:43]37.5. Wait a minute.

[01:13:48]Uh 17.5 plus 20, this value will be equal to 37.5.

[01:13:54]Right? So, what is the initial saving?

[01:13:56]25. Now, after this, after the increment in both the income and expenditure, now saving becomes how much? 37.5.

[01:14:04]Right? We have to find the percentage change in the saving.

[01:14:08]Percentage change in saving.

[01:14:13]What is the change in saving?

[01:14:16]25 and 37.5, the change is 12.5 divided by the original value is how much? 25 into 100.

[01:14:27]12.5 into two is 25. So, this is 1/2 of 100. So, change in the saving is how much? 50%.

[01:14:36]Percentage change in the saving is how much? 50%. You can see that all the problems has almost one or other. We have the same patterns that you should be very comfortable with how much? How to change percentage in the form of fraction. And the percentage change is nothing but change by original value into 100.

[01:14:53]Right? I hope all of you are clear with this.

[01:14:56]Moving to the next problem.

[01:14:59]Right, then.

[01:15:01]A man multiplied a number by 7/4 instead of 3/5.

[01:15:07]Find the percentage change in the number. Again, the find what they're asking you. Percentage change in the number. So, first what we need to find?

[01:15:14]What is the change in the number? What is the number?

[01:15:17]Uh A man multiplied a number by 7/4. So, number we can take X.

[01:15:23]Right? X, Y, or we can take any other anything because we have to find the percentage change in the number.

[01:15:28]If I solve this problem with X, the problem becomes very complicated. So, what I'll do? Anyhow, we have to multiply the number with either 7/4 or we have to multiply a number with 3/5.

[01:15:39]So, I'll take a number which is a factor of four and five. Any number you can take it, which is a multiple of four and five. Right? A number which is multiple of four and five can be either 20 or any multiple of 20. So, let's take a smaller number, 20. So, I'm assuming that let the number be let the number be 20.

[01:16:02]Why I'm taking 20? Because anyway, one way or the other, we have to find how much? We have to multiply the number with 7/4 and also we have to multiply the number with 3/5 to see the change in the number.

[01:16:14]Clear? So, I'm taking a number which is multiple of four and five. Right.

[01:16:19]So, what is the original number then?

[01:16:24]Original value should be equal to how much?

[01:16:29]Basically, the number should be multiplied by 3/5.

[01:16:35]So, 20 into 3/5.

[01:16:39]Five fours are, so four into three, 12.

[01:16:42]But by mistake, the number is multiplied by how much? 7/4.

[01:16:47]So, other value will be how much? 20 into 7/4. Four into five, five into seven is 35.

[01:16:59]So, actually, the number should be multiplied by how much? 3/5. But by mistake, the number was multiplied by how much? 7/4. So, what is the percentage change in the number we can see? So, what is the change in the number?

[01:17:11]See the change in the number. 12 and 35, the change is how much?

[01:17:16]23. So, percentage change will be equal to change. Change is how much? 23 divided by what is the initial value? 12 into 100. Whatever value we get it, that should be the answer.

[01:17:30]Four threes are 12. Four into 25.

[01:17:34]So, percentage change will be equal to 25 into 23 by three. What is the answer?

[01:17:40]25 into 23 by 3%.

[01:17:45]So, 25 into 20, how much? 500.

[01:17:50]500 plus 75, 575.

[01:17:54]Divided by 3%.

[01:17:57]Five ones are five.

[01:17:59]27.

[01:18:01]So, three ones are three, 27. Three nines are 27. Three ones are three.

[01:18:06]Then, what is left? Two.

[01:18:09]So, 191.66%.

[01:18:13]I hope you are clear with this. So, why we are taking the number as 20 here?

[01:18:17]Because that 20 must be a multiple of four as well as five.

[01:18:22]Clear? Let's move to the next problem.

[01:18:27]Fine. The price of a sugar is increased by 16 2/3% and consumption of a family is decreased by 20%. Then, find the percentage change in the expenditure.

[01:18:40]Right? Now, we know that the price into consumption.

[01:18:47]Price into consumption is equal to the expenditure.

[01:19:01]Right? So, price into consumption will always be equal to how much?

[01:19:04]Expenditure. What is given? The price of the sugar is increased by 16 2/3%. What is the meaning of 16 2/3%?

[01:19:11]16 2/3% is 1/6.

[01:19:16]What is other value? Other is 20%, which is very we are very familiar, that is 1/5.

[01:19:22]Right? We'll compare how much initial and the final value.

[01:19:27]Initial and this is the final after getting changed.

[01:19:31]Clear? Then price is increased by how much? 16 2/3% means if the initial price is six, now the final price becomes 6 + 1 which is seven. Why 6 + 1? One is the increment.

[01:19:45]So, the final after increment, what is the answer? 6 + 1 which is seven. Then and the consumption of the family decreased by 20%. So, initially if the consumption is five, now the consumption becomes how much? Four.

[01:20:00]Clear? What we need to find? Find the percentage change in the expenditure.

[01:20:05]What is expenditure in the first case? 6 * 5 30. In the second case, it is 28.

[01:20:11]What is the percentage change?

[01:20:18]Change. What is change? Two by base value is 30 into 100.

[01:20:26]2 by 30 is 1 by 15 and 1 by 15 we know that 6 2/3%.

[01:20:33]Value of 1/15 is how much? 6 of 2/3%.

[01:20:37]So, the percentage change in the expenditure will be equal to 6 2/3%.

[01:20:41]Right? I've tried my level best to cover all type of models. So, make sure that from every model at least you are solving four to five problems. If you do so, then only you'll be perfect in solving these problems. First thing again, whenever you start solving the problems based on percentage, make sure that you are very much perfect with this part. How to convert fraction in the form of percentage. At least you should know all the value from like 1/2, 1/3 so on up to 1/15.

[01:21:13]If you know all this value, the problem solving will be very very easy for all of you.

[01:21:18]Clear? This type of models have been asked in the earlier exams. This problems based on price and consumption.

[01:21:25]Clear? So, make sure that you know all this model. So, they can ask you the problems based on anything where the percentage change is there and there can be different model of the problems. I've tried my level best to cover up all the model. Okay?

[01:21:37]Then the price of the sugar is increased by 25%.

[01:21:43]Then how much percent consumption is reduced so that expenditure will remain the same? Same concept again. You know that price into consumption must be equal to expenditure.

[01:22:01]Must be equal to how much? Expenditure.

[01:22:08]What is the first criteria is given?

[01:22:10]The price of the sugar is increased by 25%. 25% means if the earlier price is how much? What is 25%? 25% is 1/4.

[01:22:30]So, so price is how much? 25% increase.

[01:22:33]So, initially price is how much? Four.

[01:22:35]After increment, the price becomes how much? Five.

[01:22:39]After increment, price price is how much? Five.

[01:22:44]What they say that how much percent consumption is reduced so that expenditure will remain the same?

[01:22:51]Then Let me see. Expenditure should remain the same.

[01:23:02]Then Let me call expenditure I'll take a value which is a multiple of four and five.

[01:23:09]A multiple of how much? Four and five.

[01:23:11]Can I take expenditure as 20?

[01:23:14]Multiple of four and five, I can take expenditure as how much? 20. We also know that price into consumption will be equal to how much? Expenditure. If the price is four part, expenditure will be equal to how much? Five part.

[01:23:28]Simple logic. Again, you can take any number here, but expenditure should be constant in both the cases. So, let's make it 20 and 20.

[01:23:36]Right? Now, price was initially four part. Now, the price after increment becomes how much? Five. Since the expenditure is how much? Constant. Can I say that this value must be equal to how much? Four.

[01:23:48]Clear? Then what they ask you so that expenditure remains fine. How much percent consumption is reduced? Right? So, we are finding how much? The percentage change in the consumption. What is the percentage change in the consumption?

[01:24:02]So, percentage change will be equal to change. What is change here? One divided by the initial value is how much? Five into 100.

[01:24:14]So, 1/5 into 100 must be equal to how much? 20%.

[01:24:19]Clear? So, what I've done? Only price is increased here. So, price is increased means if the initial price is four, after increment, the price becomes how much? Five.

[01:24:29]Since expenditure is a constant value, it is not changing. I can take any expenditure here, but I took a number which is multiple of four and five which is problem becomes easier for us.

[01:24:40]Then since price into consumption equal to expenditure, we know that here consumption should be five. Here consumption should be equal to four. The percentage change will be equal to how much? 1/5 into 100 which is 20%. Right?

[01:24:56]Fine. Again, so So, almost how much I have covered? Eight seven to eight models and make sure that all of you practice at least 10 to 15 problems based on the similar models. Right? If you'll do so that you'll be perfect in this percentage. So, next class we'll start with time and work concept. Right? Hope you'll stay tuned. I hope the class you have enjoyed the class. We'll see you in the next session.

[01:25:21]Thank you.