Question

From a class of $24$ boys, a boy aged $10$ years leaves the class and in his place a new boy is admitted. As a result the average age of the class is increased by $2$ months. What is the age of the new boys ?

• A. $6years$
• B. $8years$
• C. $10years$
• D. $12years$

Answer 1

The correct option is A $6years$

Let the average age of the class be $x$ years
Then the total age of the class $=24x$ years
New average age of the class $=$ $(x-\frac{2}{12})$ years $=$ $(x-\frac{1}{6})$ years
Let the age of the new boy be $y$ years
Given, $\frac{24x-10+y}{24}=x-\frac{1}{6}$

$\Rightarrow 24x-10+y=24x-4$

$\Rightarrow y=6$
Therefore, the age of the new boy is $6$ years.