SSC SUPER SATURDAY | SSC CGL | MATHS LIVE MOCK - 21 EXPLANATION | BY RAJ KUMAR SIR

[00:00:00]Hi, welcome to Everest Coaching Point.

[00:00:03]So, let's see the explanation of Mock Test 21, Super Saturday Mock Test 21.

[00:00:14]You can write these exams for free every Saturday. For those who don't know, if you install the Everest Impact app on our Play Store, this exam will be live for you every Friday afternoon to Saturday evening. You can write it. Watch the exam. Let's read the first question. A landlord buys a flat for 8000 pieces. He wants to get a 9% annual return on his investment after paying 2000 pieces per month for maintenance. What should be the monthly rent he charges?

[00:00:56]He wants to get a return of 9%, even if he spends 2000 monthly on maintenance, so he wants to get 9% income, that is, 9% of 8 lakhs minus the zeros, that is, he expects his income to be 72,000.

[00:01:20]How much income does he need per year, that is, how much income does he need per month? 72/12 months. He expects a monthly income of 6000. But after 2000 maintenance, this much should be left.

[00:01:33]So if he gets 6000 net monthly income, he should get 8000. If 8000 comes in, even if 2000 is lost, 6000 remains.

[00:01:43]See the next question.

[00:01:47]Look at 31q + 18q -37q + 210 When given such questions, when you are given larger numbers in cubes, the first thing you should do is check the options.

[00:02:02]If the unit digits in the options are different, the first priority is the unit digit. But here, what is the unit digit in all the options?

[00:02:08]Next Priority Approximations Next Priority Approximation 31 cube is not needed exactly. 3 cube is 27. 30 cube is 27000. 31 cube is more so it will be more. So more than 27000. More than 27000. 18 cube is 20 cube is 8000. 10 cube is 1000. So between 1000 and 8000, 18 is close to 20, so it is an approximation.

[00:02:50]Maybe 6000. If you also know the exact values, fine, even if it's an approximation, it's okay. Look at 37 cubes. 30 cubes is 27,000. 40 cubes is 64,000. So this is close to 40, so think of it as an approximation of 50,000.

[00:03:11]Next OnePlus 210, when we are dealing in 1000s, what if you ignore this 210? What are our options? Let's get close.

[00:03:19]27+6 means 33. 50,000 to 33000. Here -50,000 + 33. So what happens? 17. However, in reality, this value is not 27,000, it is a little more. We took 27, so approximately 15,000 should be in that range, so our answer would definitely be the second option.

[00:03:43]If we are given the option of more than one out of 15,000 or 16,000, then we can do a digital sum check if we want. But before that, many problems become easier through approximation. Let's look at the next question. It asks LCA LCM and HCF of two numbers are 144 and 8 respectively. One of the numbers is 16. Find the other number. Look at lcm and hcf lcm * hcf = product of the two numbers and the product of two numbers is always equal to the product of lcm and hcf lca is either 144 hcf is either 8 one number in two numbers or 16 second number we need to find out. 8 times again 2 times 72 times This is what we ask next one Look 60%A = 0.3B 3B = 1/6 a:BC You are asking 60%A means if we write everything in fraction then 60% means 3/5 or 6/5 10 Let's write because here also we have 3/10 of B 1/6 First only A and B so if we take A/B see what happens this is 12 gone 1/2 is true. If A is one part then B has a value of 2s chance this is not certain a1 then B should be 2 this is not certain this is not certain actually we got the answer directly.

[00:05:27]Actually, 60% of A is 0.3 of B, which means 30%. If you want, the A value should be lower and the B value should be higher. The A value should be lower and the B value should be higher. There is one of the options to see the original, and it is given very easily. If we want a right procedure, given this, we have a/x = b/y = c/z. If we can write it in that form, a: bc becomes x: yz. We should not have numerators, only denominators should be a/a = b/y = c/j In that form, we should write 10 What is the LCM of 10 and 6? What is the LCM of 10 and 6? Is it 30? You can cancel this now if you want 3/5 5 What is the LCM of 10 and 6? 30 If we divide everything by 30, we already have 5, write another 30.

[00:06:27]Next, we have 3b / 10, we are writing another 30.

[00:06:34]c/6, another 30.

[00:06:38]This is actually zero in all of these. We can cancel here. The 3rd cancel is canceled. A/5 equals b/10 = c/18.

[00:06:59]So we have a ratio: a: b 5: 108.

[00:07:06]First option, see the next question. What is the Average of all integers between 300 and 450 that are exactly divisible by 13. The average of all numbers between 300 and 450 that are divisible by 13 is being asked.

[00:07:25]Average is always greater than minimum value and less than maximum value. It should be greater than 300. Not this. It should be less than 450. Not these two options. The average should always be in between. It should not be less than minimum value and should not be greater than maximum value. So when we say average for numbers between 300 and 450, it should definitely be in this range. There is only one option. A number that is divisible by 13.

[00:07:55]After 300, the number that is divisible by 13 is 233, that is, 339. 399. If we add one, we get 299.

[00:08:08]260+ 52. 312. This is the first number. Also, the number that is divisible by 13 before 450 is 33.

[00:08:19]39. 39. 9. Another 60. 43. 52.

[00:08:29]So 442. It will be 3430p 52 The average of these two, the first number and the last number, the average, the overall average, will be 70 20 Sorry, this is 442, so 752 54/2 377 But they gave a lot of options, they gave it very easily, there is no real work to do.

[00:09:10]Next one, see what is the central angle of a sector with an arc length of 10 centimeters in a circle of radius 5.

[00:09:22]Length of the arc formula. When we are given an angle, the length of the arc formula is the sector length of the arc formula. l = that θ. The length of the arc is 10. The radius is 5. The θ in radians is the same. So if we go there, it will come directly in θ radians.

[00:09:43]Radians are the next one from a.

[00:09:48]64 liters container of pure spirit 8 liters are removed and replaced by water This operation is performed a total of three times What is the final quantity of spirit remaining in the container How much is being removed 8 liters are being removed Out of 64 How much is being removed How much is left I mean how much is left. The number of times you do that should be written in the power. So this is the fraction left over. 1/8 1-1/8 means 7/8 whole cube so in total mixture 343/ 512 parts we have spirit how original is total mixture is 64 we calculate that 343/52* 64 this is 8 times 8 of which 4 8 32 40 something we have only one option as an executor cancel next one see A circular pond is surrounded by a path 2 meters wide total area of ​​pond plus path total area pond one plus path total area pond plus path 616 square meters pond area is given pond area pond area 452.16 6 what is the radius of the pond actually when pond area is given radius There is no real need to calculate this. That is, if you take it, the calculations may be easy, but think normally. Here we have four options, right? Try it once. If the path is given, the area of ​​the pond is given as Iask, and it is said to be 452.16.

[00:12:15]That is all you need to do.

[00:12:17]Look at the approximation. The value above is 3.14 4 * rAsk that 452 that 3.

[00:12:27]Approximately how many times will it cancel out? 3 150s 3 150s 450 will be approximately. The value of the ask is 150. It may have a slightly lower value.

[00:12:39]Then the square root of it is approximately 12.

[00:12:45]This is our answer. If you want, you can do it.

[00:12:48]Take the value of π as 616 and subtract that value from 14. It will get 12. You can do it anyway, if it's not there, just give us this and ask us. You can try it anyway. It's just an approximation, not an exact answer.

[00:13:06]We can answer approximately because there are more differences when it comes to squares and cubes.

[00:13:11]Look at the right next question.

[00:13:15]To get 13 squared 13, your answer needs to be almost 170. So here, when you cancel, there is no chance of getting that much value. Similarly, even if you want to get 11, you need to cancel 120 times. There is a lot of difference between 120 and 150.

[00:13:34]Suppose x = 2+ 3y = 5+ 1 z = 2 2+1 Which of the following is true when we are given this, if we have to compare, especially when we give pluses, make squares. What happens to xsk? 2+ 3holes and 2+ 3holescr 2+3 5+2ab 2 6 5+2 6 Next ysk value see ysk 5+ 1holescr 5+1 6+ 2 5 6+2 5 Next zsk what happens to 2 2 2 2 +1holescr ask 2sk means 4 4*2= 8 a+1 + 2ab 2 * 2= 4 4 2 Let's say 2* 2 2*1 2 2 9+ 4 2 So clearly this is a very big number.

[00:14:51]zd is the highest next. If we observe that this is more than this There is more, but it is a little less, you can think of it as 2.236, this is approximately 2.4 4, so you have one more than one difference, so this is clearly y is bigger, if you want, you can convert it to decimals and check it, suppose there is 2 6, we want the value 6 6 as an approximation, that is, write the perfect square 4 before it, how much excess is there over 4, this is a double value in the denominator, that is, approximately 2.5 5, so 2 * 2.5 means 5 5+5 means 10, this is clearly, we get 5 value 2+ 1x, 2.25 4.5 5 is more than 10, clearly, so x<than z, first option is our answer, see next question, this is clearly much more, right? More than 13 if the average of a number and It's reciprocal is the average of the cube and its reciprocal is the average number and its reciprocal is the average of these, so they say this is 2.

[00:16:22]From that x+1/x = 4 we are told cube and its reciprocal x+1/x = m then let us discuss in the algebra table link x+1/x = m then xqya + 1/xqya = mqya -3m then x+1/a value is 4 then xcube 1/eq e mcube 4q -3* 4 which is 52 but they are asking us to calculate the average so outside of this xcube 1/eqube 52/2 52/2 which is 26 our answer next one is a cone is such that area of ​​its base equals its lateral surface area if radius is of find the slope height l. Look, base area means πr², lateral surface area is πa l slant height lpa π consol consol so l equal to what happened.

[00:17:47]Look, when the radius is small, okay, this will be our answer. The question was given, we solved it, but the answer is that we should turn off RA, but in fact, it is impossible for the slant height to be equal to the radius. The slant height must definitely be greater than R.

[00:18:09]Our answer to this question is correct, but think about it, this means it won't be a cone shape, only a circle will remain. This slot height comes down to this R. This is H. This is H.

[00:18:23]What does it mean when H is zero? But okay, for this question, we should opt for the same answer. Next, A can build up a wall in 8 days. B can break it in three days. A has worked for four days and then B joins to work with A for another day. Only in these days will A alone build the remaining part of the wall.

[00:18:50]Let's see if A can finish the work in 8 days.

[00:18:55]B can destroy it in three days.

[00:18:57]Time ratio is 8:3, but efficiency is 3:8.

[00:19:03]What will happen to the work? 24 This is what MT does, so write minus because it destroys. Look what they are saying is that A did it for four days, total work 24, A did it for four days, then B only had two days with A, so effectively speaking, A did it for four days and then B did it for another two days, so if you say A did it for six days, then B did it for six days, so it's 18 - 16 so far. The total work is 24 units of work, so if A does this work effectively, then B has to do it again. It will take 7 1/3 days to do 22 units of work with an efficiency of 3.

[00:20:02]See next one Next one Distance between centers of two circles is given as d Lens of the direct common tangent l and a is said lskpA square is given Sum of the squares of the radii is given What is the value of d Direct common tangent length formula d equals Sorry Direct common tangent length is dsk - r1 - r2s Let's say here Direct common tangent is called l Somehow square so dsk - r1 - r2hosk come on. Transversal common tangent length is what this is going to be dsk - r1 + r2sk.

[00:20:52]We're given lsk + m^2, so add these two.

[00:20:56]What happens if we add these two? If we add these two, we get 2d square. So if we add these two, we get minus. r1pA2hoskrpA1 -A2hoskr apbuskpA -Bahoskr means 2a this is lsk +a^2 how much 200 = 2d^ -2 * r1^ + r2s is this 100 means this goes there 2dsk = 400 d square value 200 d = square root 200 or 10 2 This is our answer next one express 0.12121212 and so on if any fraction is repeated we write it as recurring. To write this in p/q form, write all the visible digits minus the non-recommended digits. The denominator is the number of digits under the nines and zeros bar.

[00:22:20]If there are non-recurring digits after the decimal, zeros will appear here. If you cancel 12/99, you will get 4/33.

[00:22:34]Next one, the graph of y = 4x - 5 passes through the point at which it is asked. Just substitute the values in it and see that y -1 4* x -5 is sufficient. Let's see the second one, y = -5 4* x -5 0 -5 - The first two are satisfied, which means that there are definitely no options A and B, so this is the answer. Anyway, look at the third option y = 4 * x -5 is enough. All that is left is the next one. If sin x = 3/5, then 1p tnA /v - tnA, see if it says tnA. If you want to replace tnA, you should write sin x/ka x.

[00:23:40]1 - sin x/ka x cos x + sinn x /ka x -sin x cos x +sin x / cos x -sin x. If sin x has a value of 3/5, then cos x has a value of 3/5. If cos x has a value of 4/5, then we have to calculate cos x. Look at cos x.

[00:24:13]Since the denominator of everything is hypotenuse, it is enough to write only the numerator part, 4+3/4 -3, because the denominator of everything is 5, so this is our answer. Or you can simply say tan x is 3/5, even if you write them, it is enough. If tan x is 3/4, then it is enough to substitute that 3/4.

[00:24:41]Next one look in triangle ABC in triangle ABC in triangle ABC this line segment de is parallel to BC this line segment de parallel to BC line segment de parallel to BC with d on abb and e on a in the ratio of the area of ​​the triangle ad to the area of ​​the trapezoid ad is 4:21 so this is 4 this is 21 what is the ratio of ad to db this line is a little higher because it is just 4 this is 21 but anyway we can always form similar triangles ad is 4 if abc tell what happens abc 4+ 21 25 so the areas ratio is 4:25 so the sides ratio is always the square root of it is 4 25 so the sides The ratio is 2:5. They ask us the same thing.

[00:26:10]They ask for ad/db. 5 is the total. The length of ab is ad /db. If ab is five parts, then the length of ab is ad/db.

[00:26:26]In the question, they ask us how much ad is d. That is, if we subtract ad from abb, our answer will be 5 -2, which is 2/3.

[00:26:39]2:3 This will be our answer.

[00:26:44]Next one, which set includes numbers like -5, 0 and 6. Negative numbers have zero, are integers, right? Natural numbers start from one.

[00:27:01]Irrational numbers have roots. Whole numbers do not have negative numbers.

[00:27:06]A triangle has sides 8 centimeters and 10 centimeters. The angle between them is 120°. What is its area? Let's see. When we know two sides and know the angle between those two sides, the area formula is: sine θf is the product of the adjacent sides int sine of angle between adjacent sides. So here, one side is 8 and the other is 10 120 sun 120 g. In this, the fourth time is 4 times 40 sun 120, which means sun of 90 + 30 sun of 90 p θ means the second quadrant is positive. If the sine is 30, then 30 is 3/2.

[00:28:01]This is 20 times 20 3. This is our answer.

[00:28:12]Next one. A man spends 80% of his income.

[00:28:17]Income has increased by 25% but his expenditure remains the same. He asks how much he is spending. He is spending 80% of his income.

[00:28:32]4f Income equals expenditure plus savings. Income is 5.

[00:28:39]But expenditure is 4. Savings. How much income has increased by 25%? Income has increased by 25%, that is, 525 125.

[00:28:50]Increase in income equals increase in expenditure plus increase in savings. He is saying that expenditure remains the same.

[00:28:57]What is the increase in expenditure before? Can we say that the increase in expenditure is zero? If we multiply the current amount by how much, see here. It should come to 125. If we add these two, how much will we multiply the 125th by? We get 125. 125 is our answer. Look at the increase in income, this increase in expenditure plus the increase in savings. We are only writing increases. Don't get confused here. The expenditure is the same. If the expenditure is the same, then if there were four parts before, then we are writing it as if there are four parts now. So if the expenditure is original and there is four now, then we should write it as how much it has increased and by what percentage it has increased. So here, income has increased by 25%, so if the expenditure is the same by 25%, then we need to carefully understand what percentage increase there is. So how much do you add to Geo and you get 125? How much do you multiply Sova by and you get 125? That is our answer. The base of a prism is a rectangle. Its length is twice its width. The perimeter of the base is 30 centimeters. The perimeter of the base is 30 centimeters. The base is called a rectangle. Length is twice its width. This is x.

[00:30:21]This is 2x. The perimeter is 2x.

[00:30:29]So 6x is 6x. The value of 30 is x. The value of 5 is now seen. The prism's height decreases in arithmetic progression from 15 cm in the first layer to 9 cm in the fourth layer. What is the total volume? See prism volume formula base area * height base is a rectangle x how much 5 length how much 10 base area easy 10 * 5 lb height is not uniform in the first layer is 15 in the first layer is 9 in the last layer is 15 so if we want sum sum of n terms is n/2 * a up how many layers are there 4 /2 we know in the first layer also know in the last layer times 224 that is 48 we have to write this so if 48 is multiplied by 5 then 120 120e 10 sorry 24 then if 48 is multiplied by 5 then 240 240* 10 2400 cm multiply 48 by 5 next one d and e start a business with They say that equal investments after four months will be 10,000 at the end of the year if the total profit is 33,3000 and each share is 15,000, which was their initial investment. Let's say that the actual investment is the same as the initial investment. Suppose that the two invested x. They kept the d for four months and added an extra 10,000 for the next 8 months. This is d investment * time This is total d profit Is it b same from first to last Now in this e got 15000 profit Out of 33000 15000 Out of 33000 If we get e how much did a get 18000 This is d profit This is e profit Is this profit 15000 D profit is 18000 See zeros cancel Here four also gets cancelled In this two times four In this three times 3 In this six times 3 In this five times Multiplying 5x Here x+2a means 3x 3x e 5 15x 2 20 20e 100 Here 6* 3x means 18x 3x = 100 x = 33 1/3 This is 100 We can say 333 and so on, this will be our answer.

[00:34:06]It came in 1000s x value 33 1/3 1000 so we are writing e 1000.

[00:34:18]Next one a shopkeeper sells shirts at 500 each on one he gains 25% and on the other he loses 25% what is his net loss is in value not in percentage if selling price of these articles is same on one he gains x% and on the other he loses x% in overall transaction there is a loss of x^/1 100 i.e. 6.25% 25% loss or 1/16 loss here i.e. 16 is cost price if one is loss each is selling for 500 i.e. how much are two together selling for 1000 1000 this is cost price this is loss i.e. selling price what is 15 is selling price this is 1000 if this is one one part how much One part is how much, so 1000/15 clearly means 60 something, right? Lose 60 something, this will be our answer.

[00:35:36]66.67 67 Next One A bookstore advertises Buy Four Books and Get the Fifth at 50% Discount if the market price of each book is 480 and all books are priced the same. What is the effective percentage discount the customer receives on the total purchase? If four books are purchased, the fifth book is said to be 50%. Suppose the market price of each is 100. If it is 100, what will be the market price of five books? What is the market price of five books? Let's say 500 pieces, but how much are they selling? That is, if you buy four books, you get 50% of the fifth book, which is 4. Or if you buy one fifth book, you get 50% of the fifth book, which is 50, which is ₹450.

[00:36:42]That ₹500 is marked and sold for 450.

[00:36:48]They are selling it for 450, marked 500. That is, how much discount is given? 50 50 is the percentage of 500 * 100 So effectively 10% discount is given.

[00:37:05]This is our answer. Next, a man spends 30% of his salary on rent, 20% on groceries and 25% on other expenses. If he saves 9000, what is his salary? If it is not said that it is of the remaining amount, you can add it directly. Rent is 30% gone 20% Grocery is 50 there 25% Expenses is 75% gone 30+ 20 50+ 25 75% Expenses are gone How much is left if 75% Expenses are gone 25% This is 9000 they said 25% is 9000 but total salary is always 100% So this is four times 9000 which is four times 36000 this will be our answer