# Percentage based Simplification

Question type: Find x% of y

## Formula Method

x% of y = $( \frac{x}{100} $) × y

E.g. 30% of 70 = $( \frac{30}{100} $) × 70 = 21

## Multiplication Method

30% of 70 = 3 × 7 = 21

15% of 120 = 1.5 × 12 = 18

35% of 32 = 3.5 × 3.2 = ? (It’s hard to calculate. So, in such cases we can split the percentage or the number.)

## Splitting the percentage

45% of 90 = ?

45% = 40% + 5%

10% of 90 = 9 and 5% of 90 = 4.5

So, 45% of 90 = (9 × 4) + 4.5 = 36 + 4.5 = 40.5

OR

45% = 50% - 5%

50% of 90 = 45 and 5% of 90 = 4.5

So, 45% of 90 = 45 - 4.5

## Splitting the number

45% of 90 = ?

90 = 100 - 10

45% of 100 = 45 and 45% of 10 = 4.5

So, 45% of 90 = 45 - 4.5

###### Q. 20% of 52 = ?

Explanations :

Explanation 1: Splitting the Percentage

10% of 52 = 5.2

So, 20% of 52 = 5.2 × 2 = 10.4

10% of 52 = 5.2

So, 20% of 52 = 5.2 × 2 = 10.4

Explanation 2: Splitting the Number

20% of 50 = 10

20% of 2 = 0.4

So, 20% of 52 = 10 + 0.4 = 10.4

20% of 50 = 10

20% of 2 = 0.4

So, 20% of 52 = 10 + 0.4 = 10.4

###### Q. 35% of 32 = ?

Explanation:

10% of 32 = 3.2 and 5% of 32 = 1.6

So, 35% of 32 = (3.2 × 3) + 1.6 = 9.6 + 1.6 = 11.2

So, 35% of 32 = (3.2 × 3) + 1.6 = 9.6 + 1.6 = 11.2

###### Q. 27% of 124 = ?

Explanations :

Explanation 1:

25% of 124 = 31

2% of 124 = 2.48

27% of 124 = 31 + 2.48 = 33.48

25% of 124 = 31

2% of 124 = 2.48

27% of 124 = 31 + 2.48 = 33.48

Explanation 2:

20% of 124 = 24.8

5% of 124 = 6.2

2% of 124 = 2.48

27% of 124 = 24.8 + 6.2 + 2.48 = 33.48

20% of 124 = 24.8

5% of 124 = 6.2

2% of 124 = 2.48

27% of 124 = 24.8 + 6.2 + 2.48 = 33.48

###### Q. 60% of a number is 360. What is 99% of the same number?

Explanations :

Explanation 1: Traditional Method

Let the number be x.

Now, (60/100) × x = 360

Or x = 600

99 % of 600 = (99/100) × 600 = 594

Let the number be x.

Now, (60/100) × x = 360

Or x = 600

99 % of 600 = (99/100) × 600 = 594

Explanation 2: Unitary Method

60% of a number is 360

So, 1% of that number = 360/60

So, 99% of that number = (360/60) × 99 = 594

60% of a number is 360

So, 1% of that number = 360/60

So, 99% of that number = (360/60) × 99 = 594

Explanation 3:

60% = 360

So 10% = 60

And 100% = 600; 1% = 6

So, 99% = 100% - 1% = 600 - 6 = 594

60% = 360

So 10% = 60

And 100% = 600; 1% = 6

So, 99% = 100% - 1% = 600 - 6 = 594

But what if the data in the question is weird?

E.g. Calculate 14.28% of 63.

Then we need to know the equivalent percentage values of a few fractions.