# 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
Explanation 2: Splitting the Number
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
###### Q. 27% of 124 = ?

Explanations :

Explanation 1:
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

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

Explanations :

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
Explanation 3:
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.

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