# How much Percentage One Quantity is of Another?

Finding how much percentage one quantity is of another. Suppose there are two quantities and we want to find what percent of one quantity is of the other quantity or find how many hundredths of one quantity should be taken so that it is equal to the second quantity.

We will follow the following steps for expressing one quantity as the percentage (percent) of another quantity.

Step I: Quantity to be compared is taken as a numerator.

Step II: Quantity with which it is to be compared is taken as a denominator.

Step III: Quantities are expressed in the fraction form then the fraction is multiplied by 100 %.

Note: The two quantities must be of the same kind and must have the same units.

Suppose, we have to express x as the percentage of y; then the formula is:

Percentage = x/y × 100

Note: Both x and y must have the same units.

We will apply the concept of solving some real-life problems by using the formula for finding how much percentage one quantity is of another.

Solve examples of what percent is one number of another number:

1. Sam scored 36 marks out of 60. Express the marks in percentage.

Solution:

Therefore, required percent = (36/60 × 100) %

= 60%

2. Express 80 ml as a percent of 400 ml

Solution:

Therefore, required percent = (80/400 × 100) %

= 20 %

3. Express 1 hour 36 minutes as the percent of 2 hours 40 minutes.

Solution:

We know, 1 hour = 60 minutes.

Therefore, 1 hour 36 minutes = (60 + 36) minutes = 96 minutes and

2 hours 40 minutes = (120 + 40) minutes = 160 minutes

Required percent = (96/160 × 100) %

= 60 %

4. Find the number if 12 % of it is 60.

Solution:

Let the number be m

Then 12 % of m = 60

⇒ 12/100 × m = 60

⇒ m = (60 × 100)/12

Therefore, the required number = 500

Word problems for finding how much percentage one quantity is of another:

1. What percent of $15 is 75 cents? Solution: We know,$1 = 100 cents

\$15 = (15 × 100) cents = 1500 cents

Therefore, required percent = (75/1500 × 100) %

= 5 %

2. What percent of 70 kg is 2.1 kg?

Solution:

Required percent = (2.1 kg/70 kg × 100) %

= 210/70 %

= 3 %

Therefore, 2.1 kg is 3 % of 70 kg.

3. 296 is what per cent of 3700?

Solution:

Let m % of 3700 = 296

m/100 × 3700 = 296

m = (296 × 100)/3700

m = 29600/3700

m = 8

Therefore, 8 % of 3700 is 296.

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