Question

The average age of an adult class is $40$ years. $12$ new students with an average age of $32$ years join the class, thereby decreasing the average by $4$ years. The original strength of the class was

• A. $10$
• B. $12$
• C. $11$
• D. $15$

Answer 1

The correct option is B $12$

Let the original strength of the class be $x.$
Sum of ages of the whole class $=\left(40x\right)$ years
Sum of ages of $12$ new students $=(12\times 32)=384$ years
$\therefore \frac{40x+384}{x+12}=36$
$\Rightarrow \frac{10x+96}{x+12}=9$
$\Rightarrow 10x+96=9x+108$
$\Rightarrow x=12$
Hence, the original strength of the class was $12.$