Question

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

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

Answer: (B)

$12$

Let the original strength of the class be $x$

Then Total age of $x$ students $=40x$ years
Total age of $12$ new students $=12\times 32=384$ years
New average of $(x+12)$ students $=40-4=36$ years
Therefore, total age of $(x+12)$ students $=(x+12)\times 36=(36x+432)$years

Thus $40x+384=36x+432$

$\Rightarrow$ $4x=48$

$\Rightarrow$ $x=12$