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%.

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**8th Grade Math Practice**

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