Question

The ratio of 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:
Here, we will assume that there are \[7x\] boys and \[5x\] girls. Then we will add these numbers of boys and girls and then take it equal to 720 and simplify the obtained equation to find the value of \[x\]. Then we will substitute the above value of \[x\] in the number of girls and boys. In order to make the ratio \[1:1\], the number of girls must be equal to the number of boys. So, we will add for the number of girls to make it equal to the boys.

Complete step by step solution:
We are given that the ratio of the number of boys and girls in a school of 720 students is \[7:5\].
Let us assume that there are \[7x\] boys and \[5x\] girls.
Adding these numbers of boys and girls and then taking it equal to 720, we get
\[ \Rightarrow 7x + 5x = 720\]
Adding the left hand side of the above equation, we get
\[ \Rightarrow 12x = 720\]
Dividing the above equation by 12 on both sides, we get
\[
   \Rightarrow \dfrac{{12x}}{{12}} = \dfrac{{720}}{{12}} \\
   \Rightarrow x = 60 \\
 \]
Substituting the above value of \[x\] in the number of boys, we get
\[ \Rightarrow 7 \times 60 = 420\]
Then we will substitute the above value of \[x\] in the number of girls, we get
\[ \Rightarrow 5 \times 60 = 300\]
In order to make the ratio \[1:1\], the number of girls must be equal to the number of boys.
So, we will add 300 with 120 for the number of girls to make it equal to the boys.

Therefore, 120 girls are added for the \[1:1\] ratio.
Hence, option B is correct.

Note:
Note: We will add the number of boys and girls to find the total number of students. One needs to assume the boys and girls have the same variables or else the answer will be wrong. We can also verify our answer by taking the ratio, \[420:300\]. So we have to simplify the obtained ratio, we get $\dfrac{7}{5}$
Hence, our answer is correct.