Question

The average age of $8$ persons in a committee is increased by $2$ years when two men aged $35$ years and $45$ years are substituted by two women. What is the average age of these two women ?

• A. $54$ years
• B. $52$ years
• C. $50$ years
• D. $48$ years

Answer 1

The correct option is D $48$ years

Let the average age of $8$ persons be $x$ years

Then total age of $8$ persons $=8x$
Also let $y_1$ and $y_2$ be the ages of the two women who replaced the two men

Then $\frac{8x-35-45+(y_1+y_2)}{8}=x+2$

$\Rightarrow 8x-80+y_1+y_2=8x+16$

$\Rightarrow y_1+y_2=96$
Therefore, average age of the two women $=$ $\frac{y_1+y_2}{2}=\frac{96}{2}=48$ years