Question

There are $ 700 $ students in a school out of which $ 420 $ are girls. Find the percentage of boys in the school.

Answer 1

Hint: In the school, students include both the girls and boys. If the number of girls is given then subtracting it from the total number of students, we get the number of boys. Simply the number of boys and find its percentage using the total number of students in the school.

Complete step by step solution:
Given that the number of girls in the school are $ 420 $ girls
Total number of students are $ 700 $ students
The number of boys in the school are $ = 700 - 420 $
Simplify the above expression –
The number of boys in the school are $ = 280 $
Percentage of boys in the school is given by –
 $ = \dfrac{{280}}{{700}} \times 100 $
Find the factors for the above expression –
 $ = \dfrac{{7 \times 40}}{{7 \times 100}} \times 100 $
Common factors from the numerator and the denominator cancel each other and therefore remove $ 7 \times 100 $ from the numerator and the denominator of the above expression.
 $ = 40\% $ boys in the school
Thus, the percentage of boys in the school is $ 40\% $
So, the correct answer is “ $ 40\% $”.

Note: Be good in finding the factors of the terms. The product of the factors gives the original number. The above example can be solved by first finding the percentage of girls and then subtracting it from hundred percent and getting the number of percentages of boys.
If $ 700 = 100\% $
Then $ 420 = \% ? $
Cross multiply the above expression –
 $ = \dfrac{{420 \times 100}}{{700}} $
Remove common factors from the numerator and the denominator –
 $ = 60\% $ girls
If in the school $ 60\% $ are girls then the percentage of boys $ = 100 - 60 = 40\% $ boys