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. 12
• B. 11
• C. 10
• D. 15

Answer 1

Answer: (A)

12

Answer 2

Let the original number of students in the class be $x$.
Their total age be $40x$ (since the average age is 40 years).
When 12 new students with an average age of 32 years join, the total age of the new students is $12 \times 32 = 384$.
The new average age of the class becomes $40 - 4 = 36$.
The total number of students is now $x + 12$, and their total age is $40x + 384$.

The new average age is:

$\frac{40x + 384}{x + 12} = 36$

Multiplying both sides by $x + 12$ we get,
\Rightarrow\;$$40x + 384 = 36(x + 12)
\Rightarrow\;$$40x + 384 = 36x + 432
\Rightarrow\;$$4x = 48
\Rightarrow\;$$x = \frac{48}{4} = 12

Therefore, the original strength of the class was 12 students.