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

The correct option is B $120$

Let $x$ be the numbers of boys
and $y$ be the numbers of girls
Therefore, the equation is $x+y=720$.
Again, the ratio is $7:5$
$\frac{x}{y}=\frac{7}{5}$
$\Rightarrow x=\frac{7y}{5}$
Putting the value of $x$ in equation $x+y=720$, we get
$\frac{7y}{5}+y=720$
$\Rightarrow \frac{12y}{5}=720$
$\Rightarrow y=720\times \frac{5}{12}$
$\Rightarrow y=300$
Putting the value of $y$ in above equation, we get
$x+y=720$
$\Rightarrow x+300=720$
$\Rightarrow x=720-300$
$=420$
For ratio $1:1,x$ should be equal to $y$.
That means number of girls should be $420$
Therefore, $420-300=120$ girls must be admitted.