Question

The ratio of the number of boys and girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?
A) 100
B) 120
C) 80
D) 150

Answer 1

Hint:
Using the ratio and the total number of students we can find the present number of girls and then we will find the required number because of the ratio changes to 1:1. This required ratio means the number of boys and girls is the same.

Complete step by step solution:
Given that the total number of students =720
The ratio of boys and girls is 7:5.
Let’s first find the total number of boys and the total number of girls separately.
Total number of boys =total students \[ \times \dfrac{7}{{12}}\]
 \[
   \Rightarrow 720 \times \dfrac{7}{{12}} \\
   \Rightarrow 60 \times 7 \\
   \Rightarrow 420 \\
 \]
Total number of girls =total students \[ \times \dfrac{5}{{12}}\]
 \[
   \Rightarrow 720 \times \dfrac{5}{{12}} \\
   \Rightarrow 60 \times 5 \\
   \Rightarrow 300 \\
 \]
Or we can directly find as
Total number of girls =total students –total number of boys
                     \[
   \Rightarrow 720 - 420 \\
   \Rightarrow 300 \\
 \]
But this number is for present students. Now we need to find how many more girls are to be admitted to make the ratio 1:1.
Ratio 1:1 means the number of boys = number of girls.
Now the total number of boys student present is 420.
And girls student are only 300.
So it means we need \[420 - 300 = 120\] girls student more.

So the correct option is B.

Note:
1) They just asked the more number of girls to be admitted that does not mean the older number of girls students should not be considered.
2) We just need to find the number of more girls student along with the older one in order to make the ratio 1:1.