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

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0:00Hi, welcome to a tutorial on percentage
0:03from careerite.com.
0:04Percentage is one of the fundamentals of
0:06quantitative aptitude and hence
0:09placement test, job interviews and all
0:11competitive exams generally have four to
0:13five sums in various formats related to
0:16percentage. In this video, we learn how
0:19to tackle percentage sums easily and
0:21score in exam. For practice, you can go
0:24to careerite.com which has thousand plus
0:27aptitude questions for you. So let's
0:29start with percentage.
0:32[Music]
0:44First let us understand what do we mean
0:46by percentage. Percentage has only two
0:50simple meanings. One is percentage means
0:53part that means a part of something.
0:56Okay. And percentage has the symbol.
0:59This is the symbol of percentage and it
1:01means divide by 100. This is these are
1:05the only two meanings of percentage that
1:07we need to know to solve the sums. Okay.
1:11Percentage very simply means a part and
1:13percentage means divide by 100. So if
1:16someone says this is 25% it would simply
1:19be 25 divided by 100. This percentage
1:23symbol means divide by 100. And what do
1:25we mean by percentage? means part. For
1:27example, this is a biscuit. Okay? Now,
1:30this is a whole biscuit. This is an
1:32entire biscuit. If someone says, "Give
1:34me say 30% of the biscuit." So, you'll
1:38remove some part and give it to the
1:40other person. So, a part of the whole is
1:44nothing but percentage of the whole. The
1:47entire part is 100%. Percentage is
1:50always take considered to be 100. An
1:53entire thing a whole thing is always
1:55100%. And when we say 10% 20%, then we
1:59remove 10% 20% from this whole thing.
2:01Like here we gave 30% of the biscuit.
2:05Right? For example, if uh let us say
2:08that there there is a tank and it has
2:10say some water in it. The total amount
2:13of water in the tank is 80 L.
2:17If someone says give me 10% of the
2:19water, what does that mean? The person
2:22wants 10% of 80 L. That means 10%
2:28of 80 L right? Meaning of is
2:33multiplication. Meaning of percentage is
2:36divide by 100. So what do we get? 10
2:39upon 100. Off means multiplication. And
2:42we have 80 L over here. So this gets
2:46cancelled. This gets cancelled. So what
2:48do we get? 8 L. That means the person
2:52wants 10% of the 80 lit or 10% of the
2:55water means the person wants 8 L of
2:58water. This is the actual meaning of
3:00percentage. That means a part of a whole
3:04or if someone wants the whole thing, if
3:07someone wants the entire 80 lit, that
3:09means the person wants 100% of the water
3:12or 100% of the thing. See how simple the
3:16concept of percentage is. When we solve
3:18more and more sums, you will become more
3:21acquainted with the concept of
3:22percentage. It is very important to
3:24understand percentage because it is
3:26important from point of view of
3:28discounts. Then there's a uh chapter on
3:32profit and loss. We need it for that.
3:35Again, there are many sections in
3:37quantitative aptitude that need
3:40percentage to be clear. Okay. Now let's
3:43see what are some of the common
3:45percentages that we see and what do what
3:48are they called
3:52common percentages let us say this is a
3:55piece of bread this is an entire bread
3:58okay now the this whole thing what do we
4:01call it this is nothing but 100% that we
4:04have seen this is nothing but whole one
4:06that is one entire bread now if someone
4:09says give me half a bread Right? So how
4:13much percent bread should we give to
4:14that person? That is half of 100%.
4:20What does that mean? Half of 100%. Off
4:24means multiplication. That is 50%. That
4:28means 50% means half. Same way if
4:32someone says give me 1/3 then it would
4:34be 1 by3 into 100%, that would be 33.33
4:4133 go going on percent or we can express
4:44it as 33 1 by3%.
4:48So 33%
4:51is nothing but
4:53of the object. If someone says give me
4:561/4 of the object right? So what it
4:58would be 1x4 into 100 that is nothing
5:01but 25%.
5:03So if someone wants 25% of the object
5:06just give that person 1/4 of the object.
5:08So if someone says let's say someone
5:10wants 10% of the bread how much you'll
5:13give? So entire is 100%. Out of that the
5:17person wants 10%. So let us see how much
5:21we'll get. Okay, we need this fraction
5:23multiplied by 100%, equal to 10%, so
5:28this fraction would be 1 upon 10. So
5:31when a person wants 110th of the bread,
5:34that means that person wants 10% of the
5:37bread. If someone wants 1/4 of the
5:38bread, the person wants 25% of the
5:41bread. There's another important thing.
5:43If someone wants 1/5 of the bread, then
5:45that means the person wants 20% of the
5:50bread. So these are the common values
5:53associated with percentage. Half means
5:5550%. 1/3 is 33 1x 3. 1/4 is 25%. 1/10th
6:00is 10%. 1/5 is 20%. There are few more
6:04values. Let's note them down. What is
6:073x4? 3x 4 is nothing but 1/4. This is
6:111/4. This is three times. That is 25%
6:14plus 25% plus 25%. That is nothing but
6:1875.
6:20percent. If someone wants 1 by8 amount
6:23of bread, right? So what is that? 1x8 is
6:26nothing but 100% divided by 12.5%.
6:31So these are common percentages and they
6:33are corresponding
6:35fractions. So just remember it. So
6:38sometimes in percentages sums like word
6:41problems on percentages someone might
6:42say that this so and so person has these
6:45many things. So out of that that person
6:49gives out half of the things. So how
6:51many how much percent of the things
6:52remain. So we should know half is gone
6:54that means 50% is gone. 50% is gone that
6:57means 50% remains right. So this is very
7:01easy. Now next let us see how to
7:03calculate percentages very easily. Here
7:06we know that percentage is nothing but
7:08multiplication. Right? Let us see
7:10another technique to calculate
7:12percentages easily. Let's see how to
7:16find percentages very quickly. Okay. Now
7:19over here let us take a value say uh 260
7:24right now what is this? This is 100%.
7:27Now if someone says give me 10% of 260.
7:31So what we'll do 10% of 260 that would
7:35be 10 upon 100 multiplied office is
7:39multiplied into 260 this gets cancelled
7:42this gets cancelled you get 26. See this
7:45is easy but there's another easier
7:47method to calculate percentages like 10%
7:501% etc. What is that? Let's see 260.
7:54What is this? This is 100%. What do we
7:57want? 10%. Right? That means 1 0 is
8:00less. If 1 0 is less from from 100% to
8:0310%, 1 zero is less. This zero is not
8:06there. If 1 0 is less, what you should
8:08do? You just you just need to put a
8:11decimal point from right hand side.
8:13Okay. So, right hand side 10 is less.
8:16From right hand side, let's put one
8:17decimal point. This is 1. So, what do we
8:20get? 26.0. That is nothing but 26. This
8:23becomes 10% of 260.
8:26See how easy it was. Take any other
8:28example. Say we take 6 5 4 7 9 4. Take
8:34this number. What is 10% of this? Simply
8:36put one decimal point. This is 10%.
8:39Right? Now let us take again a example
8:42of 350. Now if someone wants 20%, what
8:46you will do? You will simply what is
8:4920%. What is 20%, that is nothing but 2
8:52into 10%, that is 2 * 10%, so find 10%,
8:5510% of 350 is put a decimal point, you
8:58get 35 multiplied by 2. 35 into 2 is
9:03nothing but 70. So 70 is nothing but 20%
9:08of 350.
9:11See how easily if you know 10%, you can
9:13find out 20%, 30%, 40% and all that
9:16stuff. Now again let's take uh another
9:20example 693.
9:23Okay this example find out 1% of this
9:27this is what this is 100% we want 1%
9:31that is there are there are two zeros
9:33less from right hand side. So put in two
9:35decimal places first decimal place
9:37second decimal place put it over here.
9:40So 6.93
9:42is 1% of 693.
9:46See you found out 1%, 10%, 20%, let's
9:49move on to a little bit difficult
9:52number, okay? Or difficult value. Say we
9:55have as usual over here we have 260 and
9:57we want 39% of this. Now what to do?
10:01Very easy. No need to panic. 39%, 39 is
10:05nearer to 40, right? So first find 40%,
10:09why? Let's see why. Okay, so let's let's
10:13calculate here somewhere at the top.
10:14Okay. So we'll have space. So 260. What
10:19is 10? We want 40%. How to calculate
10:2140%. First calculate 10%. 260. 10% is
10:2626. Multiply by 40. 4 6 are 4 6 are 24.
10:324 a 2 104 right is nothing but 40% of
10:38260. Now what do we want? We want 39%.
10:41What is 39%. 39% is nothing but 40%
10:46minus 1%. Now what is 1% of 260? 1% of
10:51260 is 2.6 because we put in two decimal
10:55places 2.6. So 104 minus 2.6. That would
10:59be 1 0 1.4.
11:03This is 39% of 260. See how orally and
11:06very quickly we were able to find out to
11:09what is 39% of 260. Otherwise you will
11:12have to do longer divisions and all that
11:14stuff. So use this trick. If someone
11:16wants 63%, look at the left hand side
11:19corner. If someone wants 63%, what
11:21you'll do? Find 60%
11:24add
11:263% into it. What is 3%? Find 1% multiply
11:30by 3. What is 60%? Find 10% multiply by
11:35six. See how easy it was. No, no issues
11:39over here. Very very very easy trick.
11:41Just remember this. It would be very
11:43useful in exam to solve sums quickly.
11:46Now let's move on to some sums related
11:48to percentage.
11:50Question number one. 56% of y is 182.
11:55What is y? Very very easy sum. Let's
11:57see. You know percentage means what?
11:59Divide by 100 of means what?
12:02Multiplication. So what they are saying?
12:0456 divided by 100 multiplied by y. 56%
12:07of y is 182. We want to find the value
12:10of y. Simply take it over here. Okay.
12:14Divide by 56. 56. This is 56. Let's say
12:19divide by 2. What you'll get? You'll get
12:2128 over here. 91 over here. Let's try
12:26some other number. This is divisible by
12:287. 7 4 are 7 1 are 7 21 13
12:34100 divided by 4. What will we get? 4 3
12:39are 12 10 2's are 8 25 325 is the
12:44answer. Y is 325.
12:49Question number two, what percent is 42
12:52kg of 336 kg? Very easy to solve. Let's
12:56see how to solve this kind of sums. Now
12:59here they have given off but that does
13:00not mean multiplication. Okay, do not
13:03multiply. What they want is that there
13:06is one quantity quantity one and there
13:08is quantity two and how much percent is
13:11first quantity of the second quantity
13:13right now generally when we have say 25%
13:16or 50% what do we do percentage symbol
13:19means divide by 100 but here we want to
13:22find percent right there is no
13:24percentage given we want to find percent
13:27when we want to find percent we multiply
13:30by 100 so let's have 100 over here
13:33multiplication ation. Okay. Now, how to
13:36arrange these two quantities? They have
13:37given off but we should not multiply
13:39right now over here. What do they mean?
13:41What do they want? Is that 42 kg is how
13:44much part of 336 kg? We have learned
13:46percentage is part. If this is the bread
13:49and someone wants say 10%, then this
13:52much percent this much amount of part
13:54would be removed. Right? So the person
13:57wants how much of how much part is 42 kg
14:01of this 336
14:03kg. So how to write that quantity 1
14:06which is the okay of which we want to
14:09find percent divided by quantity 2 that
14:12is the percentage in relation to which
14:15we want the quantity in relation to
14:16which the percentage is calculated. So
14:19we want percent of quantity 1 and with
14:22respect to quantity 2 right. So we have
14:2642 upon 36 into 100 that is nothing but
14:29this would be 20 uh 14 3's are 14 2's
14:34are 28. Okay this would be 14 2 are 28
14:3856 14 4 are 3 1 are 3 into 8. So 100
14:43upon 8 that would be 12
14:4812.5%.
14:51So 42 kg is 12.5% of 336
14:56kg. See how easy it was there are two
14:59types either divide by 100 or multiply
15:00by 100. When we want to find percent
15:02multiply by 100 and whenever they are
15:04given two quantities okay A and B. And
15:07if you want how much percent is a of b
15:11then we'll have a of b multiplied by 100
15:16and that would be our percentage. Right?
15:19We'll see some more examples of this and
15:21so this idea will become more clearer
15:23and clearer. Moving to next question.
15:27If 15% of y is same as 21% of zed then
15:3212.5% of y is equal to what% of zed?
15:36Very easy. What have they given? 15% of
15:39y is equal to 21% of zed. Then 12.5%
15:47of y is equal to how much% of zed simply
15:52cross multiply what do we get? 15%
15:56into question mark equal to 21% into
16:0112.5%.
16:03Now why could we simply cross multiply?
16:06Because we had Z zed on one side, Y Y Y
16:08Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
16:08Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
16:08Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y on
16:09one side. Okay. So we'll have question
16:11mark equal to 21 into 12.5 divided by 15
16:163 7 are 3 5 are okay. 2.5 2's are 2.5 5
16:23are 7 5 are 35 divided by 2 that would
16:27be 17.5%.
16:31That means 12.5%
16:34of Y is equal to 17.5%
16:38of zed. This is the answer. Moving to
16:42next question.
16:44Question number four. If price of rice
16:47is 30% less than that of wheat, then the
16:51price of wheat is how much percent more
16:54than that of rice? Again, very easy. In
16:56such sums, we do not know what exactly
16:58is the price. We only know the
17:00percentage. So how to solve or how to
17:02approach these kind of percentage sums?
17:04It is very easy. Always take some
17:06arbitrarily arbitrary value. The best
17:09value to take while calculating
17:10percentage is 100. Right? So let us
17:14assume that the price of rice is rupees
17:17100. Right? Now they no price of wheat
17:21is rupees 100. Right? Because they've
17:22given price of rice is 30% less. So what
17:25would be the price of rice? That would
17:28be 100 rupees minus 30% less 30% of
17:32what? 30% of wheat's price that is
17:35nothing but 100 rupees right. So 100
17:38rupees minus 30 rupees 30% of 100. How
17:42to calculate 30% of 100? Very easy two
17:45methods. 30 divided by 100 * 100. So
17:49you'll get 30 or 10% is how much? 10% of
17:53100 is 10. Multiply three times we get
17:5630. Same answer right you'll get rupees
17:5970. Now what they have given is that
18:01price of rice is 70 price of wheat is
18:04100 that we have calculated. What they
18:05have given is that price of rice that is
18:0770 is 30% less than wheat. Then how much
18:10is price of wheat? How much percent more
18:14is the price of wheat than rice? We
18:16cannot simply write since it is 30% less
18:18it would be 30% more. No the percentage
18:21value is different. Let's see what
18:23exactly is the percentage value. Now
18:26over here we want to find out how much
18:29percent more is wheat's price than the
18:32rice price. That means how much is
18:34wheat's price of rice price. Okay. And
18:38in percentage, right? So this is what we
18:41saw in the previous sum. Right? So
18:43wheat's price that is 100 rupees of the
18:47rice price that means the rice price
18:49should be in denominator. 100. A what we
18:52saw was quantity 1's percentage in
18:54relation to quantity two. Same way price
18:57of wheat in relation to price of rice
19:00and we want the percentage. So multiply
19:02by 100. What do we get? This gets
19:04cancelled, right? We have 1,000 divided
19:08by 7. 7 1's are 7 37 4 are 28 27 2 are
19:1414 67 8 are 56 475 are 35 and so on. So
19:20approximately 142.85%.
19:23See how the value of wheat is 142.85%
19:28times of rice. Now what they want they
19:30do not want how much is percentage how
19:33much is price of wheat in relation to
19:36rice. What they want? How much more is
19:38the percentage? Generally entire
19:41quantity we take it as 100%. 100% is
19:44maximum correct 100% is maximum. So how
19:48much extra is there?
19:50142.85%.
19:53Minus 100%. That would be 42.85%
19:58more. So price of wheat is 42.85% 85%
20:03more than price of rice.
20:07Correct? Now there can be another sum.
20:10They can give you price of rice and they
20:11say price of rice is 30% more than that
20:13of wheat. Then the price of wheat is how
20:16much percent less than that of rice. You
20:18have to use the same technique uh
20:20quantity 1's price divided by quantity
20:242's price multiplied by 100 to get the
20:27percentage quant price of first quantity
20:30in relation to second quantity. Right?
20:33Always remember this tip that is first
20:36quantity is percentage in relation to
20:38second quantity multiplied by 100. That
20:41will give you the percentage required
20:43percentage. Whenever they ask what is
20:45percentage of quantity 1 in relation to
20:47quantity two just divide 1 by 2 into 100
20:50that would give us percentage. Going to
20:52question number five.
20:55The price of apple is first increased by
20:5810% and then decreased by 10%. What is
21:02the change in the price of apple? Again
21:04very easy. We do not know the price. So
21:05let us assume that the price of apple is
21:08100 rupees. First the price of apple was
21:10increased by 10%. Okay, increase by 10%.
21:14What is 10% of 100? 10 rupees. So now
21:17the price of the new price, okay, will
21:20be 100 + 10 that is 110 rupees. Now the
21:25price is decreased by 10%. What is now
21:2910% of the new price that is 10% of 110
21:34simply put a decimal that is rupees 11.
21:37So 11 rupees price has been reduced
21:40right. So what is the new second price?
21:43Okay, the final price 110 minus 11 that
21:46is rupees 99. What have they asked? What
21:50is the change in the price of apple?
21:52Original price 100 rupees. Now 99 what
21:55is the change? 100 - 99 equal to rupee
21:581. So the change in price of apple is
22:01rupee 1. If you want to express it in
22:03the format of percentage what we should
22:06write how much is rupee 1? Okay, what
22:10percent is rupee 1 of rupees 100? We
22:14have seen in the previous sums quantity
22:161 percentage of quantity 1 in relation
22:19to quantity two right percentage of
22:21quantity 1 quantity 1 in relation to
22:24quantity 2 that is nothing but this this
22:27multiplied by 100 first quantity divided
22:29by second quantity multiplied by 100
22:31that would be 1%. So change in price of
22:34apple is 1% or rupee 1. Why should we
22:38not take rupee 1 but find percentage?
22:40Because here we do not know the final
22:42the actual value of price of apple. It
22:44may be 1,000 rupees, 10,000 rupees, 5
22:47rupees, 50 rupees. We do not know. So we
22:49cannot take such absolute value. We have
22:51assumed rupees 100. So we got rupees 1
22:54or rupee 1. So the change which is given
22:57over there has to be calculated in
22:59percentage because they have given
23:01percentage. Moving to question number
23:03six.
23:05If the price of a sugar is raised by
23:0825%. Then by how much percent should a
23:11person reduce his consumption of sugar
23:13so that expenditure remains same. Now
23:17over here this might look bit difficult
23:19but it is not. It is pretty easy by
23:21common sense we can easily solve this.
23:23Okay. What have they given? Expenditure
23:25which is there that should remain same.
23:28Okay. Now initially there was some
23:30expenditure. Later on after the change
23:32of price also there was some expenditure
23:34and both the expenditures should remain
23:36same. Do we know what is the price of
23:38sugar? No. So let us assume that price
23:40of sugar is rupees 100 per kg. Now this
23:43is the rate of sugar. Do we know how
23:45much the person used to consume earlier?
23:48No, we do not know. So let us assume
23:50that the person used to consume 1 kg
23:52sugar only. Okay. So what was the
23:54expenditure initially? 1 kg sugar that
23:57is quantity of sugar consumed into rate
23:59of the sugar rupees 100 per kg. This was
24:01the expenditure earlier. Now what has
24:03happened is that price increases by 25%.
24:07Initially it was 100 rupees it increased
24:10by 25%. What is 25% of 100? 25% of 100
24:17simply it is rupees 25. So the price
24:20increases by rupees 25. So what is the
24:22new price? 100 + 25 that would be rupees
24:28125. So new price becomes 125. Do we
24:31know the new consumption? No. So let us
24:33assume that new consumption is C. Okay.
24:36So let's find the value of C. That would
24:38be 100 upon 125 25 4 5 that is 0.8
24:44kg. Initially the person was eating 1
24:47kg. Now the person person should eat kg.
24:51How much less amount of sugar should be
24:54consumed by the person? So the person
24:57should reduce his quantity by 0.2 kg.
25:00Right? So that the expenditure remains
25:03same. Now this 0.2 kg is how much
25:06percent of 1 kg because we want how much
25:09percent the person should reduce right
25:11here the person reduces by absolute
25:13value of2 kg. But we want in format of
25:16percentage that is what is percentage of
25:18quantity 1 to that of quantity 2. What
25:22is it 1 by 2 into 100 right? We have
25:25seen quantity 1 by quantity 2 by 100. So
25:28what would be the answer? 0.2 divided by
25:311 into 100 that would be 20%. So if the
25:36price increases by 25% to keep the
25:38expenditure same the consumption of
25:40sugar should reduce by 20%. Moving to
25:45next question.
25:47Question number seven. Why has to score
25:5040% marks to pass? He gets 20 marks and
25:54fails by 40 marks. The maximum marks of
25:57the exam are let's see how to solve
25:59this. Okay. Let's say the maximum marks
26:02of the exam are m. Okay. And this is
26:05zero. Now to pass 40% marks are needed.
26:08So this is let's say 40%. Okay. If M is
26:11the total marks then what is 40% of M?
26:1440% of M. So 40 M upon 100. Right? This
26:22is 40 by 100 multiplied by M. So these
26:24are nothing but passing marks. Now Y
26:27gets how many marks? Y gets 20 marks.
26:31And he fails by how many marks? He fails
26:33by 40 marks. What does that mean? Had Y
26:36got 40 marks, he would have passed. That
26:38means he would have got the passing
26:40marks. That means 20 marks plus 40 marks
26:44which Y did not get since he fails by 40
26:47marks is nothing but the passing marks.
26:50Right? See if a person say this is 100.
26:55Okay, maximum marks is 100 and 35% is
26:57passing. Let us assume. And if a person
26:59gets 15% okay and fails by 20 marks or
27:05if a person gets 15 marks and fails by
27:07for fails by 20 marks what does that
27:10mean? The person has 15 marks and he got
27:1320 marks less than the passing marks.
27:15Same way over here Y gets 20 marks and
27:18fails by 40 marks. That means Y gets 40
27:21marks less than the passing marks.
27:22Passing marks are 40 m by 100. Let's
27:25calculate what do we get this upon 100
27:29this gets cancelled. Okay. So we have
27:32600 divided by 4 equal to m. So m is
27:37nothing but 4 1 are 4 25
27:42marks. So the maximum marks of the exam
27:44are
27:46150.
27:48Question number eight. A scores 10% and
27:51fails by 30 marks. B scores 40% marks
27:55and gets 30 marks more than the minimum
27:58marks needed to pass the exam. What are
28:01the maximum marks for the exam? Now this
28:03is similar sum just a step ahead. Let's
28:06see how to solve it. Now A and B are
28:07giving the same exam that means the
28:09minimum marks for both have to be same.
28:11So let us say if this is the exam and
28:13maximum marks are these. Okay, this is
28:16zero and these are maximum marks. How
28:18much does A get? A gets 10% of 10. A
28:21scores 10%, that means A gets 10% marks.
28:2410% of maximum marks. 10% of maximum
28:28marks. That is nothing but 10 upon 100
28:32multiplied by M. That is 10 m upon 100.
28:36These are the marks which A receives.
28:39Right? And it is also given that A fails
28:42by 30 marks. That means A got 30 marks
28:44less otherwise A would have got passing
28:48marks. If A would have got 30 marks, A
28:49would have got passing marks. That means
28:51what becomes the passing marks? 10 m
28:53upon 100 plus 30 marks. These become the
28:58passing marks. Right? These become the
29:01passing marks. Now what have they given?
29:04B scores 40% marks. So B gets 40% of M
29:08that is 40 M upon 100 and B gets 30
29:13marks more than minimum marks. Right? So
29:15marks of B are how much? Passing marks
29:18we already know 10 m upon 100 plus 30
29:23these are passing marks right and what
29:25have they given B gets 40% marks and for
29:29and 30 marks more than the minimum marks
29:34needed to pass that means 30 marks more
29:36has been received by B. So if if we take
29:40the score of B and we reduce 30 marks
29:42from B that means B will get passing
29:45marks. Passing marks are nothing but
29:46this. Did you understand over here?
29:49Okay. A got 10%, these are passing
29:52marks. A got 10% and 30 marks less. B
29:56got 40% and 30 marks more. So if you
30:01remove 30 marks from B's uh marks, B is
30:0540%, if you remove these 30 marks, B
30:07will get passing marks. And if we add 30
30:10marks to A's marks, A will get passing
30:13marks. both would be equal, right? So,
30:15what do we get over here? We have 10 m +
30:203,000 = 40 m - 3,000 divided by 100
30:27divided by 100 that gets cancelled. So,
30:30what do we get here? We get 6,000 would
30:34be 40 30 m. The zero gets cancelled. M
30:38equal to 200 marks. So maximum marks of
30:42the exam was 200. Let's check whether we
30:45have calculated properly or not. 10% of
30:47200 is what? So A will get 20 marks. He
30:51fails by 30 marks. So 20 + 30 is 50. So
30:5650 is the passing marks, right? As per
30:58A's condition. Now B gets 40% marks.
31:01Okay. What is 40% of 200? It is nothing
31:03but 80 marks, right? And B also gets 30
31:07marks more than minimum marks. So
31:09subtract 30. What do we get? 50. So this
31:11should be passing marks. So that is same
31:13as this. So did you understand the
31:15logic? This is nothing but both of them
31:18we have what we did was that we equated
31:21passing marks. Here A got 30 marks less
31:24than passing marks. So we added and we
31:26got the passing marks. Here B got 30
31:28marks more than passing marks. So we
31:29subtracted and we got the passing marks
31:31and we equated them. Very easy. Okay.
31:35Moving on to next sum.
31:38Question number nine. In a class, 15% of
31:40total number of students failed in
31:42science. 25% of total number of students
31:45failed in maths. 10% of total number of
31:48students failed in both. How much
31:50percent of students passed in both maths
31:52and science? Again, very very easy sum.
31:55There's a very small technique to solve
31:58this these kind of sums. These are very
32:00popular in exams. Okay. So, let us see
32:02how to solve this with a diagram. Very
32:05it's very easy. You don't have to do
32:07anything much over here. Now what have
32:09they given? They given that 10 15% of
32:12students fail in science. Let us assume
32:13these this circle represents the number
32:16of students who failed in science. How
32:17many failed in science? 15%.
32:20This circle represents students failing
32:22in maths. How many failed? 25%. Now
32:25you'll understand why I drew these
32:27circles intersecting each other. Okay?
32:3010% failed in both subjects. So 10% will
32:33come over here. this 10% failed in
32:36science as well as maths right so that
32:40is the reason when when I drew these
32:42circles they intersected each other so
32:45these 10% failed in science and maths
32:47both now how much percent of students
32:49passed in both maths and science let's
32:52see what common mistake everyone does
32:54what do they do people who passed what
32:57do they do people who passed means 100%
33:00is the total students minus what how
33:03many students students failed we'll get
33:05the pass percentage. Okay, this is
33:07correct. After that what they do they
33:09start finding out how many students
33:11failed. They what they calculate? Okay,
33:1325% failed in science, 15% failed in
33:17maths. So total 40% students failed.
33:21Correct? So how what is the pass
33:23percentage? They take 100 minus 40 equal
33:25to 60%. So 60% students passed both in
33:28maths and science. Very wrong. This is
33:31the wrong answer. This is the wrong
33:32approach. You need to see that there is
33:35a 10% given over here. These students
33:38failed both science and maths. So what
33:41happens is that this when you count 15%
33:44you're counting this 10% also. And when
33:47you're counting 25%, you're counting
33:48this 10% also. So 10% is getting counted
33:52here 10% is there. Here 10% is there.
33:55Look at that. Look at the right hand
33:56side. Here 10% is there. Here 10% is
33:59there. That means there is double
34:00counting. So we have to remove one 10%.
34:03So how many students failed? First 15%
34:07science right then 25% maths. Okay. Now
34:1110% has been counted two times. Once
34:14over here once over here. So remove one
34:1710%. Right? What you will get? 40 - 10
34:21equal to 30%. So 30% students failed.
34:25How many passed? 100% minus 30% is 70%.
34:3070% students passed in both science and
34:35maths. Moving to next question.
34:39Question number 10. By 20% decrease in
34:42the price of rice, people can buy 10 kg
34:45more rice in rupees 100. What is the
34:48original price of 1 kg of rice? Now
34:51again very very easy sum. Let's see how
34:53to solve it. It is similar to the
34:55consumption sum which we saw earlier.
34:57Okay, but let's solve this again as a
34:59new sum. Let's not rely on anything on
35:01previously. Okay, now do we know
35:04original price of rice 1 kg of rice
35:06original rate? No. Let us assume that
35:08original rate of rice is t rupees p per
35:11kg. Okay. Now what have they given is
35:15that initially in 100 rupees people were
35:17used to buy people could buy some amount
35:19of rice. Do we know that amount? No. Let
35:21us assume that people used to buy 8 kg
35:23of rice. Correct? Now because of change
35:28in price people were able to buy 10 kg
35:30more right in that same 100 rupees. What
35:32does that mean? 100 rupees remains same.
35:36So expenditure which is there 100 rupees
35:39it is remaining same. Now what is
35:41expenditure? We have seen expenditure is
35:43nothing but amount of rice. Initially it
35:45was a kg right into what is the rate of
35:48the rice? Initially it was p rupees per
35:51kg rupees p per kg that we have assumed.
35:54Okay. Now in the second case when price
35:56was decreased how much amount of rice
35:58people used were able to buy a plus 10
36:01kg because 10 kg more was possible for
36:03them in the same 100 rupees what was the
36:06price let's see now over here initial
36:08price is P 20% decrease is there in the
36:12price okay so 20% of P the price is
36:17reduced by 20% of P that is 20 upon 100
36:21into P that is nothing but 0.2 2 P. So
36:25price reduces by 0.2 P rupees. So what
36:28is the final price now? P minus 0.2P
36:31rupees. That is nothing but 0.8 P
36:34rupees. This is the price new price. So
36:38put it over here. So now we know the
36:41expenditure is same. Let's calculate. P
36:45gets canled over here. What do we have?
36:47A equal to 0.8 A + 10 into.8 is 8. Okay,
36:53here we get 0.28
36:56is equal to 8. A would be equal to 8
36:59upon.2
37:0180 upon 2 that is nothing but 40. So 40
37:04kg rice was possible for people to buy
37:07initially in rupees 100. So what would
37:10be the rate of price rate of rice or the
37:13original price of rice that is nothing
37:15but total amount total cost divided by
37:19total amount of rice. So bill divided by
37:22the rice taken that would be 2.5
37:26rupees per kg. So rice was 2.5 rupees
37:30per kg originally. Okay. And because of
37:32that people used to buy 40 kg rice in
37:35100 rupees. Moving to question number
37:3811.
37:39In an election which was contested by
37:42two candidates, one candidate got 40% of
37:46total votes and yet lost by 1,000 votes.
37:50What is the total number of votes casted
37:52in an election? Again, very very easy.
37:54Let's see. There were two candidates.
37:55The first candidate, the second
37:57candidate, first candidate got 40% of
38:00the total votes. Let us assume that the
38:02total votes, let see over here. Let us
38:05assume that the total votes that were
38:07casted were A. Okay. So, candidate one
38:10got 40% of A votes. So, that would be 40
38:15A upon 100, right? These were the votes
38:18cast which candidate one got. Now there
38:21were only two candidates. Is that right?
38:24Yes. There was there any bogus voting or
38:26anything like that? Is is it given over
38:28there? No. There were two candidates.
38:30One got 40%. So remaining 60% who will
38:33get the second candidate. Second
38:35candidate got 60% votes. So second
38:39candidate got 60A upon 100 votes. Now
38:43what have they given is that the
38:44candidate who got 40% he lost by,000
38:47votes. That means the second candidate
38:49got 1,000 votes more than the first
38:52candidate. So
38:54the first candidate okay got less
38:57thousand,000 votes less than the first
39:00than the second candidate. Right? So
39:03first candidate plus,000 votes is
39:05nothing but the second candidate. Right?
39:08This is 100. This is again 100. Let's
39:11calculate. Let's see what the answer is.
39:1340 a + 1,000
39:17into 100 divided by 100 would be equal
39:21to 60 a upon 100. This gets cancelled.
39:25So we have 1,000 into 100 = 20 a 20 5
39:32are a is 5,000. So 5,000 votes were
39:36casted in the election. Moving to next
39:40question.
39:41Question number 12. In a country 55%
39:45population is female. 80% of the male
39:48population is literate. How much of the
39:51females are literate if the total
39:53literacy is 58%. Again very easy. We do
39:56not know population. So let us assume
39:57that the population is 100. Out of that
40:00how many are females? 55% are females.
40:04That means 55% of 100. that is 55% of
40:09100 is nothing but 55. So 55 females are
40:13there. So how many males are there now?
40:15That is 100 minus 55 females that is 45
40:20males. What have they given? 80% of the
40:23male population is literate. That means
40:25literate males are nothing but 80% of
40:28male population. What is male
40:29population? 45. So 80% of 45 are
40:33literate. So what do we get? 80 upon 100
40:37into 45 right 5 2's are 5 9 are 2 4's
40:43are 4 9 are 36 so 36 males are literate
40:48okay these are literate means what have
40:50they given on the right hand side they
40:51have given that the total literacy which
40:53is there is 58% total literacy is 58%
40:58that means out of 100 people 58% people
41:01are literate that means 58% % of 100
41:06since it is total literacy that is 58
41:09people are literate out of 100 correct.
41:12Now if 58 people are literate out of 100
41:16right we know that female literates plus
41:20male literates is nothing but the total
41:23literate population of the country. We
41:26know total literate population of the
41:27country 58. We have just calculated it
41:30right. We know the male literate
41:32population of the country 36. So what is
41:35the female literate population of the
41:37country? It is 58 - 36 22. So 22 females
41:42out of 55 females are literate. Now what
41:46we have to find is how much of females
41:48are literate. Okay in percentage we have
41:51to find out find out. Why do we have to
41:53find out in percentage? Because no
41:55concrete value of population is given.
41:57So we cannot write just 22 over here. We
41:59have everything is given in percentage.
42:01So answer has to be in percentage. Let's
42:04find out the percentage that is how much
42:07percent is quantity one of quantity two.
42:12How much percent of literate how much
42:14percent is literate women of total women
42:19or how much percent is literate female
42:21to total female that is nothing but
42:23quantity 1 upon quantity 2. And since we
42:26want percentage so multiply by 100 what
42:29do we get? 11 2's are 11 5 are 5 into 2
42:3420 40%.
42:36So 40% females are literate. Moving on.
42:42If 20% of an electricity bill is
42:45deducted then rupees 100 is still to be
42:49paid. How much was the original bill?
42:51That means there was some original bill.
42:54Out of that 20% was reduced. Okay.
42:56Deducted, subtracted. So how much
42:58remains if 20% has been reduced? 80%
43:01will has to be paid. Correct? And they
43:03have said that after reducing 20%, still
43:06the person has to pay rupees 100. That
43:09means 80% of the original bill is
43:13nothing but rupees 100. 80% of 80% of
43:20the original bill let it be B is nothing
43:22but 100 what do we get over here 2 4 are
43:272 5 B is equal to 500
43:30upon 4 what will you get over here
43:35125 rupees original bill is 125 rupees
43:38see how easy it was moving to question
43:40number 14
43:42A's salary is 50% more than B's
43:46How much percent is B's salary less than
43:50A's? Again, we do not know the salary.
43:52So, let us assume that B's salary is
43:55rupees 100. What is A's salary? 50%
44:01more that is 50% of 100 that is nothing
44:06but 50 rupees
44:09more that would be 100 plus 50 rupees
44:12that would be rupees 150. So salary of A
44:15is 150 rupees. Salary of B is 100
44:19rupees. Now what we have to find how
44:20much percent is B's salary less than
44:24A's. Okay, this is not how much percent
44:27is B's salary as compared to A's salary.
44:30If that would have been case, what would
44:31have done? Quantity 1 upon quantity 2
44:34into 100. It would have been very easy.
44:37But no, this is not the case. What do we
44:39want? How much percent is B's salary
44:42less than A's salary? Okay. Now here we
44:45know A's salary is 150, B's is 100. That
44:47means B has 50 rupees less salary.
44:52Right? So this change 50 rupees less.
44:55Now we have to express it into
44:57percentage as compared to a salary. So
45:00quantity one as compared to quantity
45:04two. What is quantity two? A is salary
45:06that is 150. And we want percentage. So
45:09100 what do we get? 50 upon 150 into 100
45:14that is this is 3 that would be 100 by 3
45:17that is 33.33
45:20so on percentage or you can write 33
45:241x3%. So B's salary is 33 1x3% less than
45:29that of A. Let's revise this again.
45:31Let's see what the difference was from
45:33the previous sums here. Initially what
45:35we wanted what is 42 kg of 336 kg that
45:41means what is one quantity as compared
45:43to other quantity here what we want how
45:46much less is one quantity as compared to
45:49other quantity less that less which is
45:51there that makes us subtract the value
45:54and take only the difference and we have
45:57to take as compared to the second
45:59quantity right so we have 50 rupees that
46:02is so B salary is 50 rupees less so we
46:0550 divided by a salary into 100 and we
46:08got 33 1x3%.
46:11Moving to next question.
46:13Two numbers are less than a third number
46:16by 30% and 37%.
46:19How much percent is the second number
46:22less than the first? Now two numbers are
46:24less by 30% and 37% respectively. So let
46:28the third number be 100. So the first
46:32number is 30% less. So first number is
46:35nothing but 100 minus 30% of the third
46:39number right that is nothing but 30 100
46:42minus 30 is 70. So the first number is
46:4470 second number is 37% less 100 minus
46:5037% of
46:53100 right 37% of 100 that would be
46:57nothing but 63%. So 100 minus oh 37% of
47:01100 is 37. So 100 - 37 is 63. So 63 is
47:05the second number, 70 is the first
47:07number and third number is 100. Now we
47:09want to find out how much percent is
47:12second number less than first. So this
47:14is like the previous sum. The less
47:16quantity is there. How much is second
47:18number less than the first? 70 - 63
47:21equal to 7. So second number is seven
47:24less than the first number. And we have
47:26to find how much less how much percent
47:29less it is. So for percent what we do
47:32multiply by 100 how much less it is
47:34seven as compared to what first number.
47:36So what is the first number 70 what do
47:39we get? This gets canceled this gets
47:41canceled we get 10%. So the second
47:44number is 10% less than the first
47:46number. See did you understand the
47:48concept of less percent less than the
47:51first? You just have to subtract take
47:53the difference and then find the
47:55percentage. Otherwise we have to take
47:56first quantity divide by second quantity
47:58and find the percentage. Moving to
48:01question number 16.
48:0310% of inhabitants of a village having
48:06died of collera a panic set in during
48:09which 25% of the remaining inhabitants
48:12left the village. The population is then
48:14reduced to 4050 that is 4,50. The number
48:18of inhabitants originally was okay again
48:21very easy. Do we know the population of
48:23the village? No. Let us assume m was the
48:25population of the village. 10% died of
48:27collera. So how many remain? 100 minus
48:3010%. So 90% remain that is 90% of m. So
48:37population that remained was 90 m upon
48:40100 these many remained. Okay. Now what
48:44they have given out of the remaining
48:46that is out of this 90 90m upon 100 25
48:49left the village 25% left the village.
48:52If 25%
48:54left, how many% are remaining still in
48:57the village? 100%.
49:00Minus 25% that would be 75% of the
49:05remaining people of the remaining people
49:09remain in the village that is nothing
49:10but 75 upon 100 because percentage is
49:13divide by 100 multiply and this is off
49:17means multiply and this is nothing but
49:18the remaining people. So these many
49:20people still are left in the village.
49:24Still are remain still remained in the
49:27village. Now over here why did we take
49:29100% - 25%. Why did not we take 90% -
49:3325%. See percentage is always subtracted
49:36from what? From 100%. Here they have not
49:40said overall 25% left. What they said
49:42was that whatever is the remaining
49:44population out of that 25% left. So
49:47remaining population now we have to
49:48consider as 100% out of that 25% left
49:52and 75% remained. So remaining people
49:55are 75 upon 100 into 90 m upon 100 but
49:58they have already given population was
50:00after these 25% left population was
50:03reduced to 450 that means 4,50 people
50:07were only left in the village that is
50:09nothing but this value. So these two are
50:11equal. Let's calculate. Let's see what
50:14we get the value as. This gets
50:16cancelled. 9 1's are 9 4 are 36 459 5
50:21are 450
50:23over here. Okay. So what do we have? 25
50:26into 3 25 into 4. So let's solve what do
50:30we get? M = 450
50:34* 4 * 10 divided by 3. 3 1's are 5 are
50:41150. Okay. 15 150 into 4 600 6,000.
50:46So total population originally was 6,000
50:50inhabitants. See how easy percentage is.
50:53You don't have to do anything. You just
50:54have to remember that you have to
50:56multiply. Percentage means divide by
50:58100. Use common logic. Just read the
51:00question and you will be able to solve
51:03all the sums related to percentage in
51:05under 1 minute. Some of them might even
51:08take hardly 20 seconds. With practice,
51:11you will be able to solve guaranteed
51:13you'll be able to solve all percentage
51:15sums in hardly 45 seconds. It should not
51:19go above 1 minute. Very easy. This is
51:22very easy topic and helpful for scoring.
51:25This is it for percentage tips and
51:27tricks. If you liked it, please give it
51:30a like and share it with others. You can
51:32also leave your comments and suggestions
51:33below. Do let us know if you have some
51:36topic in mind and we will develop a
51:37video on it for you. Don't forget to
51:40subscribe to our channel and stay
51:41updated for more such tutorials.

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