Question

The ratio of number of boys of that of girls in a school of $720$ students is $7:5$. How many girls should be admitted to make the ratio $1:1$?

• A. $90$
• B. $120$
• C. $220$
• D. $100$

Answer 1

The correct option is B $120$

Given ratio of boys to girls in a school is $7:5$ with total students $720$.

Let present boys be $b$ and girls be $g$ and the girls to be admitted to make ratio $1:1$ be $g_a$.

$b=7k,g=5k$ .....(Given)

Thus total$=b+g=720$

$\Rightarrow b+g=7k+5k=720$

$\Rightarrow 12k=720$

$\Rightarrow k=\frac{720}{12}=60$

We know $b=7k=420$

and $g=5k=300$

$b=g+g_a$ .....(Given ratio is $1:1$ after admitting)

$g_a=b-g$

$g_a=420-300=120$

Therefore, $120$ girls are to be admitted to make the ratio of boys to girls $1:1$

Option (B) is correct