Percentage - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

Hi, welcome to a tutorial on percentage from careerite.com. Percentage is one of the fundamentals of quantitative aptitude and hence placement test, job interviews and all competitive exams generally have four to five sums in various formats related to percentage. In this video, we learn how to tackle percentage sums easily and score in exam. For practice, you can go to careerite.com which has thousand plus aptitude questions for you. So let's start with percentage. [Music] First let us understand what do we mean by percentage. Percentage has only two simple meanings. One is percentage means part that means a part of something. Okay. And percentage has the symbol. This is the symbol of percentage and it means divide by 100. This is these are the only two meanings of percentage that we need to know to solve the sums. Okay. Percentage very simply means a part and percentage means divide by 100. So if someone says this is 25% it would simply be 25 divided by 100. This percentage symbol means divide by 100. And what do we mean by percentage? means part. For example, this is a biscuit. Okay? Now, this is a whole biscuit. This is an entire biscuit. If someone says, "Give me say 30% of the biscuit." So, you'll remove some part and give it to the other person. So, a part of the whole is nothing but percentage of the whole. The entire part is 100%. Percentage is always take considered to be 100. An entire thing a whole thing is always 100%. And when we say 10% 20%, then we remove 10% 20% from this whole thing. Like here we gave 30% of the biscuit. Right? For example, if uh let us say that there there is a tank and it has say some water in it. The total amount of water in the tank is 80 L. If someone says give me 10% of the water, what does that mean? The person wants 10% of 80 L. That means 10% of 80 L right? Meaning of is multiplication. Meaning of percentage is divide by 100. So what do we get? 10 upon 100. Off means multiplication. And we have 80 L over here. So this gets cancelled. This gets cancelled. So what do we get? 8 L. That means the person wants 10% of the 80 lit or 10% of the water means the person wants 8 L of water. This is the actual meaning of percentage. That means a part of a whole or if someone wants the whole thing, if someone wants the entire 80 lit, that means the person wants 100% of the water or 100% of the thing. See how simple the concept of percentage is. When we solve more and more sums, you will become more acquainted with the concept of percentage. It is very important to understand percentage because it is important from point of view of discounts. Then there's a uh chapter on profit and loss. We need it for that. Again, there are many sections in quantitative aptitude that need percentage to be clear. Okay. Now let's see what are some of the common percentages that we see and what do what are they called common percentages let us say this is a piece of bread this is an entire bread okay now the this whole thing what do we call it this is nothing but 100% that we have seen this is nothing but whole one that is one entire bread now if someone says give me half a bread Right? So how much percent bread should we give to that person? That is half of 100%. What does that mean? Half of 100%. Off means multiplication. That is 50%. That means 50% means half. Same way if someone says give me 1/3 then it would be 1 by3 into 100%, that would be 33.33 33 go going on percent or we can express it as 33 1 by3%. So 33% is nothing but of the object. If someone says give me 1/4 of the object right? So what it would be 1x4 into 100 that is nothing but 25%. So if someone wants 25% of the object just give that person 1/4 of the object. So if someone says let's say someone wants 10% of the bread how much you'll give? So entire is 100%. Out of that the person wants 10%. So let us see how much we'll get. Okay, we need this fraction multiplied by 100%, equal to 10%, so this fraction would be 1 upon 10. So when a person wants 110th of the bread, that means that person wants 10% of the bread. If someone wants 1/4 of the bread, the person wants 25% of the bread. There's another important thing. If someone wants 1/5 of the bread, then that means the person wants 20% of the bread. So these are the common values associated with percentage. Half means 50%. 1/3 is 33 1x 3. 1/4 is 25%. 1/10th is 10%. 1/5 is 20%. There are few more values. Let's note them down. What is 3x4? 3x 4 is nothing but 1/4. This is 1/4. This is three times. That is 25% plus 25% plus 25%. That is nothing but 75. percent. If someone wants 1 by8 amount of bread, right? So what is that? 1x8 is nothing but 100% divided by 12.5%. So these are common percentages and they are corresponding fractions. So just remember it. So sometimes in percentages sums like word problems on percentages someone might say that this so and so person has these many things. So out of that that person gives out half of the things. So how many how much percent of the things remain. So we should know half is gone that means 50% is gone. 50% is gone that means 50% remains right. So this is very easy. Now next let us see how to calculate percentages very easily. Here we know that percentage is nothing but multiplication. Right? Let us see another technique to calculate percentages easily. Let's see how to find percentages very quickly. Okay. Now over here let us take a value say uh 260 right now what is this? This is 100%. Now if someone says give me 10% of 260. So what we'll do 10% of 260 that would be 10 upon 100 multiplied office is multiplied into 260 this gets cancelled this gets cancelled you get 26. See this is easy but there's another easier method to calculate percentages like 10% 1% etc. What is that? Let's see 260. What is this? This is 100%. What do we want? 10%. Right? That means 1 0 is less. If 1 0 is less from from 100% to 10%, 1 zero is less. This zero is not there. If 1 0 is less, what you should do? You just you just need to put a decimal point from right hand side. Okay. So, right hand side 10 is less. From right hand side, let's put one decimal point. This is 1. So, what do we get? 26.0. That is nothing but 26. This becomes 10% of 260. See how easy it was. Take any other example. Say we take 6 5 4 7 9 4. Take this number. What is 10% of this? Simply put one decimal point. This is 10%. Right? Now let us take again a example of 350. Now if someone wants 20%, what you will do? You will simply what is 20%. What is 20%, that is nothing but 2 into 10%, that is 2 * 10%, so find 10%, 10% of 350 is put a decimal point, you get 35 multiplied by 2. 35 into 2 is nothing but 70. So 70 is nothing but 20% of 350. See how easily if you know 10%, you can find out 20%, 30%, 40% and all that stuff. Now again let's take uh another example 693. Okay this example find out 1% of this this is what this is 100% we want 1% that is there are there are two zeros less from right hand side. So put in two decimal places first decimal place second decimal place put it over here. So 6.93 is 1% of 693. See you found out 1%, 10%, 20%, let's move on to a little bit difficult number, okay? Or difficult value. Say we have as usual over here we have 260 and we want 39% of this. Now what to do? Very easy. No need to panic. 39%, 39 is nearer to 40, right? So first find 40%, why? Let's see why. Okay, so let's let's calculate here somewhere at the top. Okay. So we'll have space. So 260. What is 10? We want 40%. How to calculate 40%. First calculate 10%. 260. 10% is 26. Multiply by 40. 4 6 are 4 6 are 24. 4 a 2 104 right is nothing but 40% of 260. Now what do we want? We want 39%. What is 39%. 39% is nothing but 40% minus 1%. Now what is 1% of 260? 1% of 260 is 2.6 because we put in two decimal places 2.6. So 104 minus 2.6. That would be 1 0 1.4. This is 39% of 260. See how orally and very quickly we were able to find out to what is 39% of 260. Otherwise you will have to do longer divisions and all that stuff. So use this trick. If someone wants 63%, look at the left hand side corner. If someone wants 63%, what you'll do? Find 60% add 3% into it. What is 3%? Find 1% multiply by 3. What is 60%? Find 10% multiply by six. See how easy it was. No, no issues over here. Very very very easy trick. Just remember this. It would be very useful in exam to solve sums quickly. Now let's move on to some sums related to percentage. Question number one. 56% of y is 182. What is y? Very very easy sum. Let's see. You know percentage means what? Divide by 100 of means what? Multiplication. So what they are saying? 56 divided by 100 multiplied by y. 56% of y is 182. We want to find the value of y. Simply take it over here. Okay. Divide by 56. 56. This is 56. Let's say divide by 2. What you'll get? You'll get 28 over here. 91 over here. Let's try some other number. This is divisible by 7. 7 4 are 7 1 are 7 21 13 100 divided by 4. What will we get? 4 3 are 12 10 2's are 8 25 325 is the answer. Y is 325. Question number two, what percent is 42 kg of 336 kg? Very easy to solve. Let's see how to solve this kind of sums. Now here they have given off but that does not mean multiplication. Okay, do not multiply. What they want is that there is one quantity quantity one and there is quantity two and how much percent is first quantity of the second quantity right now generally when we have say 25% or 50% what do we do percentage symbol means divide by 100 but here we want to find percent right there is no percentage given we want to find percent when we want to find percent we multiply by 100 so let's have 100 over here multiplication ation. Okay. Now, how to arrange these two quantities? They have given off but we should not multiply right now over here. What do they mean? What do they want? Is that 42 kg is how much part of 336 kg? We have learned percentage is part. If this is the bread and someone wants say 10%, then this much percent this much amount of part would be removed. Right? So the person wants how much of how much part is 42 kg of this 336 kg. So how to write that quantity 1 which is the okay of which we want to find percent divided by quantity 2 that is the percentage in relation to which we want the quantity in relation to which the percentage is calculated. So we want percent of quantity 1 and with respect to quantity 2 right. So we have 42 upon 36 into 100 that is nothing but this would be 20 uh 14 3's are 14 2's are 28. Okay this would be 14 2 are 28 56 14 4 are 3 1 are 3 into 8. So 100 upon 8 that would be 12 12.5%. So 42 kg is 12.5% of 336 kg. See how easy it was there are two types either divide by 100 or multiply by 100. When we want to find percent multiply by 100 and whenever they are given two quantities okay A and B. And if you want how much percent is a of b then we'll have a of b multiplied by 100 and that would be our percentage. Right? We'll see some more examples of this and so this idea will become more clearer and clearer. Moving to next question. If 15% of y is same as 21% of zed then 12.5% of y is equal to what% of zed? Very easy. What have they given? 15% of y is equal to 21% of zed. Then 12.5% of y is equal to how much% of zed simply cross multiply what do we get? 15% into question mark equal to 21% into 12.5%. Now why could we simply cross multiply? Because we had Z zed on one side, Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y on one side. Okay. So we'll have question mark equal to 21 into 12.5 divided by 15 3 7 are 3 5 are okay. 2.5 2's are 2.5 5 are 7 5 are 35 divided by 2 that would be 17.5%. That means 12.5% of Y is equal to 17.5% of zed. This is the answer. Moving to next question. Question number four. If price of rice is 30% less than that of wheat, then the price of wheat is how much percent more than that of rice? Again, very easy. In such sums, we do not know what exactly is the price. We only know the percentage. So how to solve or how to approach these kind of percentage sums? It is very easy. Always take some arbitrarily arbitrary value. The best value to take while calculating percentage is 100. Right? So let us assume that the price of rice is rupees 100. Right? Now they no price of wheat is rupees 100. Right? Because they've given price of rice is 30% less. So what would be the price of rice? That would be 100 rupees minus 30% less 30% of what? 30% of wheat's price that is nothing but 100 rupees right. So 100 rupees minus 30 rupees 30% of 100. How to calculate 30% of 100? Very easy two methods. 30 divided by 100 * 100. So you'll get 30 or 10% is how much? 10% of 100 is 10. Multiply three times we get 30. Same answer right you'll get rupees 70. Now what they have given is that price of rice is 70 price of wheat is 100 that we have calculated. What they have given is that price of rice that is 70 is 30% less than wheat. Then how much is price of wheat? How much percent more is the price of wheat than rice? We cannot simply write since it is 30% less it would be 30% more. No the percentage value is different. Let's see what exactly is the percentage value. Now over here we want to find out how much percent more is wheat's price than the rice price. That means how much is wheat's price of rice price. Okay. And in percentage, right? So this is what we saw in the previous sum. Right? So wheat's price that is 100 rupees of the rice price that means the rice price should be in denominator. 100. A what we saw was quantity 1's percentage in relation to quantity two. Same way price of wheat in relation to price of rice and we want the percentage. So multiply by 100. What do we get? This gets cancelled, right? We have 1,000 divided by 7. 7 1's are 7 37 4 are 28 27 2 are 14 67 8 are 56 475 are 35 and so on. So approximately 142.85%. See how the value of wheat is 142.85% times of rice. Now what they want they do not want how much is percentage how much is price of wheat in relation to rice. What they want? How much more is the percentage? Generally entire quantity we take it as 100%. 100% is maximum correct 100% is maximum. So how much extra is there? 142.85%. Minus 100%. That would be 42.85% more. So price of wheat is 42.85% 85% more than price of rice. Correct? Now there can be another sum. They can give you price of rice and they say price of rice is 30% more than that of wheat. Then the price of wheat is how much percent less than that of rice. You have to use the same technique uh quantity 1's price divided by quantity 2's price multiplied by 100 to get the percentage quant price of first quantity in relation to second quantity. Right? Always remember this tip that is first quantity is percentage in relation to second quantity multiplied by 100. That will give you the percentage required percentage. Whenever they ask what is percentage of quantity 1 in relation to quantity two just divide 1 by 2 into 100 that would give us percentage. Going to question number five. The price of apple is first increased by 10% and then decreased by 10%. What is the change in the price of apple? Again very easy. We do not know the price. So let us assume that the price of apple is 100 rupees. First the price of apple was increased by 10%. Okay, increase by 10%. What is 10% of 100? 10 rupees. So now the price of the new price, okay, will be 100 + 10 that is 110 rupees. Now the price is decreased by 10%. What is now 10% of the new price that is 10% of 110 simply put a decimal that is rupees 11. So 11 rupees price has been reduced right. So what is the new second price? Okay, the final price 110 minus 11 that is rupees 99. What have they asked? What is the change in the price of apple? Original price 100 rupees. Now 99 what is the change? 100 - 99 equal to rupee 1. So the change in price of apple is rupee 1. If you want to express it in the format of percentage what we should write how much is rupee 1? Okay, what percent is rupee 1 of rupees 100? We have seen in the previous sums quantity 1 percentage of quantity 1 in relation to quantity two right percentage of quantity 1 quantity 1 in relation to quantity 2 that is nothing but this this multiplied by 100 first quantity divided by second quantity multiplied by 100 that would be 1%. So change in price of apple is 1% or rupee 1. Why should we not take rupee 1 but find percentage? Because here we do not know the final the actual value of price of apple. It may be 1,000 rupees, 10,000 rupees, 5 rupees, 50 rupees. We do not know. So we cannot take such absolute value. We have assumed rupees 100. So we got rupees 1 or rupee 1. So the change which is given over there has to be calculated in percentage because they have given percentage. Moving to question number six. If the price of a sugar is raised by 25%. Then by how much percent should a person reduce his consumption of sugar so that expenditure remains same. Now over here this might look bit difficult but it is not. It is pretty easy by common sense we can easily solve this. Okay. What have they given? Expenditure which is there that should remain same. Okay. Now initially there was some expenditure. Later on after the change of price also there was some expenditure and both the expenditures should remain same. Do we know what is the price of sugar? No. So let us assume that price of sugar is rupees 100 per kg. Now this is the rate of sugar. Do we know how much the person used to consume earlier? No, we do not know. So let us assume that the person used to consume 1 kg sugar only. Okay. So what was the expenditure initially? 1 kg sugar that is quantity of sugar consumed into rate of the sugar rupees 100 per kg. This was the expenditure earlier. Now what has happened is that price increases by 25%. Initially it was 100 rupees it increased by 25%. What is 25% of 100? 25% of 100 simply it is rupees 25. So the price increases by rupees 25. So what is the new price? 100 + 25 that would be rupees 125. So new price becomes 125. Do we know the new consumption? No. So let us assume that new consumption is C. Okay. So let's find the value of C. That would be 100 upon 125 25 4 5 that is 0.8 kg. Initially the person was eating 1 kg. Now the person person should eat kg. How much less amount of sugar should be consumed by the person? So the person should reduce his quantity by 0.2 kg. Right? So that the expenditure remains same. Now this 0.2 kg is how much percent of 1 kg because we want how much percent the person should reduce right here the person reduces by absolute value of2 kg. But we want in format of percentage that is what is percentage of quantity 1 to that of quantity 2. What is it 1 by 2 into 100 right? We have seen quantity 1 by quantity 2 by 100. So what would be the answer? 0.2 divided by 1 into 100 that would be 20%. So if the price increases by 25% to keep the expenditure same the consumption of sugar should reduce by 20%. Moving to next question. Question number seven. Why has to score 40% marks to pass? He gets 20 marks and fails by 40 marks. The maximum marks of the exam are let's see how to solve this. Okay. Let's say the maximum marks of the exam are m. Okay. And this is zero. Now to pass 40% marks are needed. So this is let's say 40%. Okay. If M is the total marks then what is 40% of M? 40% of M. So 40 M upon 100. Right? This is 40 by 100 multiplied by M. So these are nothing but passing marks. Now Y gets how many marks? Y gets 20 marks. And he fails by how many marks? He fails by 40 marks. What does that mean? Had Y got 40 marks, he would have passed. That means he would have got the passing marks. That means 20 marks plus 40 marks which Y did not get since he fails by 40 marks is nothing but the passing marks. Right? See if a person say this is 100. Okay, maximum marks is 100 and 35% is passing. Let us assume. And if a person gets 15% okay and fails by 20 marks or if a person gets 15 marks and fails by for fails by 20 marks what does that mean? The person has 15 marks and he got 20 marks less than the passing marks. Same way over here Y gets 20 marks and fails by 40 marks. That means Y gets 40 marks less than the passing marks. Passing marks are 40 m by 100. Let's calculate what do we get this upon 100 this gets cancelled. Okay. So we have 600 divided by 4 equal to m. So m is nothing but 4 1 are 4 25 marks. So the maximum marks of the exam are 150. Question number eight. A scores 10% and fails by 30 marks. B scores 40% marks and gets 30 marks more than the minimum marks needed to pass the exam. What are the maximum marks for the exam? Now this is similar sum just a step ahead. Let's see how to solve it. Now A and B are giving the same exam that means the minimum marks for both have to be same. So let us say if this is the exam and maximum marks are these. Okay, this is zero and these are maximum marks. How much does A get? A gets 10% of 10. A scores 10%, that means A gets 10% marks. 10% of maximum marks. 10% of maximum marks. That is nothing but 10 upon 100 multiplied by M. That is 10 m upon 100. These are the marks which A receives. Right? And it is also given that A fails by 30 marks. That means A got 30 marks less otherwise A would have got passing marks. If A would have got 30 marks, A would have got passing marks. That means what becomes the passing marks? 10 m upon 100 plus 30 marks. These become the passing marks. Right? These become the passing marks. Now what have they given? B scores 40% marks. So B gets 40% of M that is 40 M upon 100 and B gets 30 marks more than minimum marks. Right? So marks of B are how much? Passing marks we already know 10 m upon 100 plus 30 these are passing marks right and what have they given B gets 40% marks and for and 30 marks more than the minimum marks needed to pass that means 30 marks more has been received by B. So if if we take the score of B and we reduce 30 marks from B that means B will get passing marks. Passing marks are nothing but this. Did you understand over here? Okay. A got 10%, these are passing marks. A got 10% and 30 marks less. B got 40% and 30 marks more. So if you remove 30 marks from B's uh marks, B is 40%, if you remove these 30 marks, B will get passing marks. And if we add 30 marks to A's marks, A will get passing marks. both would be equal, right? So, what do we get over here? We have 10 m + 3,000 = 40 m - 3,000 divided by 100 divided by 100 that gets cancelled. So, what do we get here? We get 6,000 would be 40 30 m. The zero gets cancelled. M equal to 200 marks. So maximum marks of the exam was 200. Let's check whether we have calculated properly or not. 10% of 200 is what? So A will get 20 marks. He fails by 30 marks. So 20 + 30 is 50. So 50 is the passing marks, right? As per A's condition. Now B gets 40% marks. Okay. What is 40% of 200? It is nothing but 80 marks, right? And B also gets 30 marks more than minimum marks. So subtract 30. What do we get? 50. So this should be passing marks. So that is same as this. So did you understand the logic? This is nothing but both of them we have what we did was that we equated passing marks. Here A got 30 marks less than passing marks. So we added and we got the passing marks. Here B got 30 marks more than passing marks. So we subtracted and we got the passing marks and we equated them. Very easy. Okay. Moving on to next sum. Question number nine. In a class, 15% of total number of students failed in science. 25% of total number of students failed in maths. 10% of total number of students failed in both. How much percent of students passed in both maths and science? Again, very very easy sum. There's a very small technique to solve this these kind of sums. These are very popular in exams. Okay. So, let us see how to solve this with a diagram. Very it's very easy. You don't have to do anything much over here. Now what have they given? They given that 10 15% of students fail in science. Let us assume these this circle represents the number of students who failed in science. How many failed in science? 15%. This circle represents students failing in maths. How many failed? 25%. Now you'll understand why I drew these circles intersecting each other. Okay? 10% failed in both subjects. So 10% will come over here. this 10% failed in science as well as maths right so that is the reason when when I drew these circles they intersected each other so these 10% failed in science and maths both now how much percent of students passed in both maths and science let's see what common mistake everyone does what do they do people who passed what do they do people who passed means 100% is the total students minus what how many students students failed we'll get the pass percentage. Okay, this is correct. After that what they do they start finding out how many students failed. They what they calculate? Okay, 25% failed in science, 15% failed in maths. So total 40% students failed. Correct? So how what is the pass percentage? They take 100 minus 40 equal to 60%. So 60% students passed both in maths and science. Very wrong. This is the wrong answer. This is the wrong approach. You need to see that there is a 10% given over here. These students failed both science and maths. So what happens is that this when you count 15% you're counting this 10% also. And when you're counting 25%, you're counting this 10% also. So 10% is getting counted here 10% is there. Here 10% is there. Look at that. Look at the right hand side. Here 10% is there. Here 10% is there. That means there is double counting. So we have to remove one 10%. So how many students failed? First 15% science right then 25% maths. Okay. Now 10% has been counted two times. Once over here once over here. So remove one 10%. Right? What you will get? 40 - 10 equal to 30%. So 30% students failed. How many passed? 100% minus 30% is 70%. 70% students passed in both science and maths. Moving to next question. Question number 10. By 20% decrease in the price of rice, people can buy 10 kg more rice in rupees 100. What is the original price of 1 kg of rice? Now again very very easy sum. Let's see how to solve it. It is similar to the consumption sum which we saw earlier. Okay, but let's solve this again as a new sum. Let's not rely on anything on previously. Okay, now do we know original price of rice 1 kg of rice original rate? No. Let us assume that original rate of rice is t rupees p per kg. Okay. Now what have they given is that initially in 100 rupees people were used to buy people could buy some amount of rice. Do we know that amount? No. Let us assume that people used to buy 8 kg of rice. Correct? Now because of change in price people were able to buy 10 kg more right in that same 100 rupees. What does that mean? 100 rupees remains same. So expenditure which is there 100 rupees it is remaining same. Now what is expenditure? We have seen expenditure is nothing but amount of rice. Initially it was a kg right into what is the rate of the rice? Initially it was p rupees per kg rupees p per kg that we have assumed. Okay. Now in the second case when price was decreased how much amount of rice people used were able to buy a plus 10 kg because 10 kg more was possible for them in the same 100 rupees what was the price let's see now over here initial price is P 20% decrease is there in the price okay so 20% of P the price is reduced by 20% of P that is 20 upon 100 into P that is nothing but 0.2 2 P. So price reduces by 0.2 P rupees. So what is the final price now? P minus 0.2P rupees. That is nothing but 0.8 P rupees. This is the price new price. So put it over here. So now we know the expenditure is same. Let's calculate. P gets canled over here. What do we have? A equal to 0.8 A + 10 into.8 is 8. Okay, here we get 0.28 is equal to 8. A would be equal to 8 upon.2 80 upon 2 that is nothing but 40. So 40 kg rice was possible for people to buy initially in rupees 100. So what would be the rate of price rate of rice or the original price of rice that is nothing but total amount total cost divided by total amount of rice. So bill divided by the rice taken that would be 2.5 rupees per kg. So rice was 2.5 rupees per kg originally. Okay. And because of that people used to buy 40 kg rice in 100 rupees. Moving to question number 11. In an election which was contested by two candidates, one candidate got 40% of total votes and yet lost by 1,000 votes. What is the total number of votes casted in an election? Again, very very easy. Let's see. There were two candidates. The first candidate, the second candidate, first candidate got 40% of the total votes. Let us assume that the total votes, let see over here. Let us assume that the total votes that were casted were A. Okay. So, candidate one got 40% of A votes. So, that would be 40 A upon 100, right? These were the votes cast which candidate one got. Now there were only two candidates. Is that right? Yes. There was there any bogus voting or anything like that? Is is it given over there? No. There were two candidates. One got 40%. So remaining 60% who will get the second candidate. Second candidate got 60% votes. So second candidate got 60A upon 100 votes. Now what have they given is that the candidate who got 40% he lost by,000 votes. That means the second candidate got 1,000 votes more than the first candidate. So the first candidate okay got less thousand,000 votes less than the first than the second candidate. Right? So first candidate plus,000 votes is nothing but the second candidate. Right? This is 100. This is again 100. Let's calculate. Let's see what the answer is. 40 a + 1,000 into 100 divided by 100 would be equal to 60 a upon 100. This gets cancelled. So we have 1,000 into 100 = 20 a 20 5 are a is 5,000. So 5,000 votes were casted in the election. Moving to next question. Question number 12. In a country 55% population is female. 80% of the male population is literate. How much of the females are literate if the total literacy is 58%. Again very easy. We do not know population. So let us assume that the population is 100. Out of that how many are females? 55% are females. That means 55% of 100. that is 55% of 100 is nothing but 55. So 55 females are there. So how many males are there now? That is 100 minus 55 females that is 45 males. What have they given? 80% of the male population is literate. That means literate males are nothing but 80% of male population. What is male population? 45. So 80% of 45 are literate. So what do we get? 80 upon 100 into 45 right 5 2's are 5 9 are 2 4's are 4 9 are 36 so 36 males are literate okay these are literate means what have they given on the right hand side they have given that the total literacy which is there is 58% total literacy is 58% that means out of 100 people 58% people are literate that means 58% % of 100 since it is total literacy that is 58 people are literate out of 100 correct. Now if 58 people are literate out of 100 right we know that female literates plus male literates is nothing but the total literate population of the country. We know total literate population of the country 58. We have just calculated it right. We know the male literate population of the country 36. So what is the female literate population of the country? It is 58 - 36 22. So 22 females out of 55 females are literate. Now what we have to find is how much of females are literate. Okay in percentage we have to find out find out. Why do we have to find out in percentage? Because no concrete value of population is given. So we cannot write just 22 over here. We have everything is given in percentage. So answer has to be in percentage. Let's find out the percentage that is how much percent is quantity one of quantity two. How much percent of literate how much percent is literate women of total women or how much percent is literate female to total female that is nothing but quantity 1 upon quantity 2. And since we want percentage so multiply by 100 what do we get? 11 2's are 11 5 are 5 into 2 20 40%. So 40% females are literate. Moving on. If 20% of an electricity bill is deducted then rupees 100 is still to be paid. How much was the original bill? That means there was some original bill. Out of that 20% was reduced. Okay. Deducted, subtracted. So how much remains if 20% has been reduced? 80% will has to be paid. Correct? And they have said that after reducing 20%, still the person has to pay rupees 100. That means 80% of the original bill is nothing but rupees 100. 80% of 80% of the original bill let it be B is nothing but 100 what do we get over here 2 4 are 2 5 B is equal to 500 upon 4 what will you get over here 125 rupees original bill is 125 rupees see how easy it was moving to question number 14 A's salary is 50% more than B's How much percent is B's salary less than A's? Again, we do not know the salary. So, let us assume that B's salary is rupees 100. What is A's salary? 50% more that is 50% of 100 that is nothing but 50 rupees more that would be 100 plus 50 rupees that would be rupees 150. So salary of A is 150 rupees. Salary of B is 100 rupees. Now what we have to find how much percent is B's salary less than A's. Okay, this is not how much percent is B's salary as compared to A's salary. If that would have been case, what would have done? Quantity 1 upon quantity 2 into 100. It would have been very easy. But no, this is not the case. What do we want? How much percent is B's salary less than A's salary? Okay. Now here we know A's salary is 150, B's is 100. That means B has 50 rupees less salary. Right? So this change 50 rupees less. Now we have to express it into percentage as compared to a salary. So quantity one as compared to quantity two. What is quantity two? A is salary that is 150. And we want percentage. So 100 what do we get? 50 upon 150 into 100 that is this is 3 that would be 100 by 3 that is 33.33 so on percentage or you can write 33 1x3%. So B's salary is 33 1x3% less than that of A. Let's revise this again. Let's see what the difference was from the previous sums here. Initially what we wanted what is 42 kg of 336 kg that means what is one quantity as compared to other quantity here what we want how much less is one quantity as compared to other quantity less that less which is there that makes us subtract the value and take only the difference and we have to take as compared to the second quantity right so we have 50 rupees that is so B salary is 50 rupees less so we 50 divided by a salary into 100 and we got 33 1x3%. Moving to next question. Two numbers are less than a third number by 30% and 37%. How much percent is the second number less than the first? Now two numbers are less by 30% and 37% respectively. So let the third number be 100. So the first number is 30% less. So first number is nothing but 100 minus 30% of the third number right that is nothing but 30 100 minus 30 is 70. So the first number is 70 second number is 37% less 100 minus 37% of 100 right 37% of 100 that would be nothing but 63%. So 100 minus oh 37% of 100 is 37. So 100 - 37 is 63. So 63 is the second number, 70 is the first number and third number is 100. Now we want to find out how much percent is second number less than first. So this is like the previous sum. The less quantity is there. How much is second number less than the first? 70 - 63 equal to 7. So second number is seven less than the first number. And we have to find how much less how much percent less it is. So for percent what we do multiply by 100 how much less it is seven as compared to what first number. So what is the first number 70 what do we get? This gets canceled this gets canceled we get 10%. So the second number is 10% less than the first number. See did you understand the concept of less percent less than the first? You just have to subtract take the difference and then find the percentage. Otherwise we have to take first quantity divide by second quantity and find the percentage. Moving to question number 16. 10% of inhabitants of a village having died of collera a panic set in during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050 that is 4,50. The number of inhabitants originally was okay again very easy. Do we know the population of the village? No. Let us assume m was the population of the village. 10% died of collera. So how many remain? 100 minus 10%. So 90% remain that is 90% of m. So population that remained was 90 m upon 100 these many remained. Okay. Now what they have given out of the remaining that is out of this 90 90m upon 100 25 left the village 25% left the village. If 25% left, how many% are remaining still in the village? 100%. Minus 25% that would be 75% of the remaining people of the remaining people remain in the village that is nothing but 75 upon 100 because percentage is divide by 100 multiply and this is off means multiply and this is nothing but the remaining people. So these many people still are left in the village. Still are remain still remained in the village. Now over here why did we take 100% - 25%. Why did not we take 90% - 25%. See percentage is always subtracted from what? From 100%. Here they have not said overall 25% left. What they said was that whatever is the remaining population out of that 25% left. So remaining population now we have to consider as 100% out of that 25% left and 75% remained. So remaining people are 75 upon 100 into 90 m upon 100 but they have already given population was after these 25% left population was reduced to 450 that means 4,50 people were only left in the village that is nothing but this value. So these two are equal. Let's calculate. Let's see what we get the value as. This gets cancelled. 9 1's are 9 4 are 36 459 5 are 450 over here. Okay. So what do we have? 25 into 3 25 into 4. So let's solve what do we get? M = 450 * 4 * 10 divided by 3. 3 1's are 5 are 150. Okay. 15 150 into 4 600 6,000. So total population originally was 6,000 inhabitants. See how easy percentage is. You don't have to do anything. You just have to remember that you have to multiply. Percentage means divide by 100. Use common logic. Just read the question and you will be able to solve all the sums related to percentage in under 1 minute. Some of them might even take hardly 20 seconds. With practice, you will be able to solve guaranteed you'll be able to solve all percentage sums in hardly 45 seconds. It should not go above 1 minute. Very easy. This is very easy topic and helpful for scoring. This is it for percentage tips and tricks. If you liked it, please give it a like and share it with others. You can also leave your comments and suggestions below. Do let us know if you have some topic in mind and we will develop a video on it for you. Don't forget to subscribe to our channel and stay updated for more such tutorials.