# Percentage of the given Quantity

How to find the percentage of the given quantity?

We know, a percentage is a fraction with denominator as 100 i.e. % = 1/100. Therefore, to determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.

We will follow the following steps for finding a percentage of a given number:

Step I: Obtain the number. Let the number be m.

Step II: Obtain the required percentage. Let it be R %.

Step III: To find R % of m, multiply m by R and then divide by 100; i.e. R % of m = R/100 × m

Following examples will help us to find the percentage of the given quantity using the above procedure.

Solved examples to find percent of a given number:

1. Find 40 % of 240

Solution:

We know that R % of m is equal to R/100 × m.

So, we have 40 % of 240

40/100 × 240

= 96

2. 10 % of 1 hour

Solution:

We know that R % of m is equal to R/100 × m.

So, we have 10 % of 1 hour

10 % of 60 minutes (Since, 1 hour = 60 minutes)

= 10/100 × 60 minutes

= 6 minutes

3. Find 15 % of $250. Solution: We know that R % of m is equal to R/100 × m. So, we have 15 % of$250.

15/100 × 250

= $75/2 =$37.5

4. Find 120 % of 25 km

Solution:

120 % of 25 km

= (120/100 × 25) km

= 30 km

5. Find 10 % of 400 kg

Solution:

10 % of 400 kg

= (10/100 × 400) kg

= 40 kg

6. Find the number whose 8 % is 72.

Solution:

Let the required number be m, then

8 % of m = 72

⇒ 8/100 × m = 72

⇒ m = 72 × 100/8

m = 900

Therefore, the required number is 900.

Word problems to find the percentage of the given quantity:

7. What is the sum of the money of which 15 % of $225? Solution: Let the required sum of money be$m.

15 % of $m =$225

⇒ 15/100 × m = 225

⇒ m = (225 × 100)/15

⇒ m = 1500

Therefore, sum of the money = \$1500

8. In a public show 75 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?

Solution:

First process:

75 % of 600

= 75/100 × 600

= 450

Therefore, the number of vacant seats = 600 - 450 = 150.

Second process:

Total percentage of seats = 100.

Percentage of filled seats = 75.

Therefore, percentage of vacant seats = 100 – 75 = 25.

25 % of 600

= 25/100 × 600

= 150.

Thus, the number of vacant seats is 150.

Note: Total is always 100%.

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Solved Examples on Percentage

Problems on Percentage

Real Life Problems on Percentage

Word Problems on Percentage

Application of Percentage

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