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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