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Percentage, which is clear by the name, implies “for every hundred”. This concept is actually developed to make the comparison of fractions easier by equalizing the denominators of all fractions to a hundred. (Read article “Profit and Loss”) OR In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred.

Now, let’s try to find out some weird percentages in an interesting way.

e.g. 1. What is the value of 42.22% of 63?

Ans- We can easily find 1%, 10% and 50% of any number (Because 50% of any number is just half of it). Here

1% → 0.63

2% → 1.26 (twice of 1%)

0.2% → 0.126

0.02% → 0.0126

10% → 6.3

40% → 6.3 × 4 = 25.20

So, 40% + 2% + 0.2% + 0.02% = 42.22%

Hence, 42% of 63 = 25.2 + 1.26 + 0.126 + 0.0126 = 26.5986

Let’s take another example.

e.g. 2. What is the value of 93.75% of 96?

Ans- 100% – 93.75% = 6.25%.

So, in case of 96,

10% → 9.6

5% → 4.8 (half of 10%)

2.5% → 2.4 (half of 5%)

0.25% → 0.24

1% → 0.96

So, 5% + 1% + 0.25% = 6.25%

So, 100% – 6.25% = 96 – (4.8 + 0.96 + 0.24) = 96 – 6 = 90

Hence, 93.75% of 96 is 90.

This seems a little bit confusing and complicated. But if you try this several times, you will understand the ease of this method and start loving it. The best thing about this method it, you will never find any percentage problem complicated. Even if the question is to find 42.84% of 91. You can easily find that without doing the actual and lengthy calculation including multiplication of 42.84 with 91.

Let’s take another example.

e.g. 3. Find the value of 72.96% of 75?

Ans- Here is the most interesting part. Since we know that 75 is 3/4th part of 100 and 72.96% of 75 is equal to 75% of 72.96 (because both can be written as (72.96 × 75)/100). So, instead of finding 72.96% of 75, we should find 75% of 72.96, which is,

⇒ ¾ × 72.96 = 3 × 18.24 = 54.72

Now, let’s just understand a table to do these types of questions.

Fraction          Percentage value        Fraction          Percentage Value

1/1                  100%                           1/11                            9.0909%

1/2                  50%                             1/12                            8.333%

1/3                  33.333%                      1/13                            7.69%

1/4                  25%                             1/14                            7.14%

1/5                  20%                             1/15                            6.666%

1/6                  16.666%                      1/16                            6.25%

1/7                  14.28%                        1/17                            5.88%

1/8                  12.5%                          1/18                            5.555%

1/9                  11.111%                      1/19                            5.26%

1/10                10%                             1/20                            5%

To learn this table, just remember these clue points.

  • 1 to 1/5 are easy to learn because we are using them since our childhood.
  • 1/10 and 1/20 are also easy to learn.
  • 1/6 and 1/8 are just half of 1/3 and 1/4 respectively. Similarly, 1/12 and 1/16 are just half of 1/6 and 1/8 respectively i.e. the value of 1/3 and ¼ divided by 4 respectively.
  • 1/7 = 14.28%. We can learn it easily because 14 is double of 7 and 28 is double of 14.
  • 1/9 is 11.11% and 1/11 is 09.09%, so these are easy to remember.
  • 1/14 and 1/18 are just half of 1/7 and 1/9.
  • 1/15 is 1/5 divided by 3 or 1/3 divided by 5. If you remember anyone of them, you can easily find 1/15 in just 3 or 4 seconds.
  • So, we are left with 1/13, 1/17 and 1/19. These are just 3 values; you have to learn them but you can because these are just 3 values. After using them 3 or 4 times, you will never forget them.

Let’s take some examples.

e.g. 4. Find 42.84% of 91. Ans- Here, we can see that 84 is double of 42 and there is only 1 fraction in which this doubling concept applied i.e. 1/7. Now, we just have to check whether 42 is divisible by 14 or not. Yes, it is 3 times of 14, so, 42.84% will be 3 times of 1/7. So, 42.84% of 91 = 3/7 × 91 = 3 × 13 = 39.

e.g. 5. Find 37.5% of 32.

Ans- 37.5 is clearly three times of 12.5 (as 36 is three times of 12 and also there is only one case which ends with .5 which is 12.5). So, 37.5 is also 3 times of 1/8.

So, 37.5% of 24 = 3/8 × 24 = 3 × 3 = 9.

e.g. 6. Find 87.5% of 96.

Ans- Here, 100 – 87.5 = 12.5

So, 87.5% = 1 – 1/8 = 7/8

So, 87.5% of 96 = 7/8 × 96 = 7 × 12 = 84.

e.g. 7. Find 83.33% of 120.

Ans- First we should check the approx. value. 80 is 5 times of 16. And 1/6 is 16.666, also, they have .33, so now we have to check whether 16.666 × 5 is 83.33 or not. Yes, it is. So,

83.33% of 120 = 5/6 × 120 = 5 × 20 = 100

(Also, 8.333% is 1/12, so 83.33% is 10/12 which is 5/6.)

e.g. 8. Find 36.36% of 165.

Ans- There are only 2 fractions which give us repeated digits even when multiplied by the number more than 2 and less than them. These are 1/9 and 1/11. So, if 36.36 is divided by 9, then it is multiple of 1/11 and if it is divided by 11, then it is multiple of 1/9.

Here, it is divided by 9 (i.e. 4 times 9 is 36)

So, 36.36% of 165 = 4/11 × 165 = 4 × 15 = 20.

e.g. 9. Find 44.44% of 72.

Ans- Here, 44 is divided by 11. So, it is the multiple of 1/9.

So, 44.44% of 72 = 4/9 × 72 = 4 × 8 = 32.

e.g. 10. Find the value of 93.75% of 96.

Ans- Here, 100% – 93.75% = 6.25% which is 1/16.

So, 93.75% = 1 – 1/16 = 15/16

So, 93.75% of 96 = 15/16 × 96 = 15 × 6 = 90.

e.g. 11. Find the value of 42.22% of 63.

Ans- We can break it in 2 parts. 42.22% = 20% + 22.22%.

So, 20% is 1/5 and 22.22% is 2/9 (Since 22 is the multiple of 11).

So, 42.22% of 63 = (1/5 + 1/9) × 63 = 63/5 + 126/9 = 12.6 + 14 = 26.6

(In example 1, the answer was 26.5986, which is pretty much close to 26.6)

So, we have two methods now to find percentages. You can use any of them which one you can find easier.

We were finding here percentages by a fraction but we can also find the decimal value of fraction by percentages.

e.g. 12. Find the decimal value of 7/17.

Ans- We know that 1/17 is 5.88%, which means 1/17 = 0.0588.

So, 7/17 = 7 × 0.0588 = 0.4116

e.g. 13. Find the decimal value of 5/13.

Ans- We know that 1/13 is 7.69%, which means, 1/13 = 0.0769.

So, 5/13 = 0.0769 × 5 = 0.3845

Tip: Just take any number at random, try to multiply it by any number at random, try to find any percent of any random number and then check it by the calculator. It will improve your calculation a lot.