Question

The average age of boys and girls in a class is 18. If the average age of boys in that class is 20 and that of girls is 17, then find the ratio of the number of girls to the number of boys in that class.

• A. 5 : 2
• B. 2 : 1
• C. 2 : 5
• D. 1 : 2

Answer 1

The correct option is B 2 : 1

Given,
The average age of boys = 20
The average age of girls = 17
Average age consisting both = 18

Given,
The number of boys = $x$
and the number of girls = $y$

According to the question,
$\frac{\text{(The sum of the age of boys)}}{x}=20$
$\therefore \text{The age of x boys}=20x$

$\frac{\text{(The sum of the age of girls)}}{y}=17$
$\therefore \text{The age of y girls}=17y$

$\text{and}\frac{\text{((The sum of the age of boys)+(The sum of the age of girls))}}{(x+y)}=18$

$\Rightarrow \frac{20x+17y}{x+y}=18$
$\Rightarrow 20x+17y=18x+18y$
$\Rightarrow 2x=y$
$\Rightarrow \frac{2}{1}=\frac{y}{x}$

Therefore, the ratio of the number of girls to the number of boys is 2:1.