Question

In a school, 10% of the boys are the same in number as one-fourth of the girls. What is the ratio of boys to girls in that school?
(A) $3:2$
(B) $5:2$
(C) $2:1$
(D) $4:3$

Answer 1

Hint: First assume that the number of boys and the number of girls as a variable and then find the 10% of boys and one-fourth of the girls. Then apply the given condition that 10% of the boys are the same in number as one-fourth of the girls nad it will give the desired result.

Complete step-by-step answer:
We have given the problem that 10% of the boys are the same in number as one-fourth of the girls in a school.
The goal of the problem is to find the ratio of boys to girls in that school.
First, assume that the number of boys and girls in the school are $x$ and $y$ respectively.
Then, find 10% of the boys in the school as:
$10\% {\text{ of }}x = \dfrac{{10}}{{100}} \times x$
$ \Rightarrow 10\% {\text{ of }}x = \dfrac{x}{{10}}$
As we assumed that the number of girls in the class is $y$, then one-fourth of the girls are given as:
One-fourth of the girls$ = \dfrac{1}{4}\left( y \right)$
One-fourth of the girls$ = \dfrac{y}{4}$
Then according to the question, it is given that 10% of boys are same as one-fourth of girls in the school, then
10% of boys = one-fourth of girls
Substitute the values calculated above, into the equation:
$\dfrac{x}{{10}} = \dfrac{y}{4}$
$ \Rightarrow \dfrac{x}{y} = \dfrac{{10}}{4}$
$ \Rightarrow \dfrac{x}{y} = \dfrac{5}{2}$
So, the ratio of the boys to the girls in the school is $5:2$.
Therefore, the option (B) is correct.

Note: The ratio is applicable in the comparison of two or more quantities. It shows how much of one thing is compared to the other thing. We have found the ratio of the boys to the girls as $5:2$, it means that there are 5 boys in every 2 girls in the school.