Question : The average age of 15 members of a committee is increased by 4 years when two members whose ages are 60 years and 70 years are replaced by two new members. What is the average age of the new members?
Option 1: 105 years
Option 2: 80 years
Option 3: 85 years
Option 4: 95 years
Correct Answer: 95 years
Solution :
Let the average age of 15 members of a committee be $x$.
The sum of ages of 15 members = $15x$
New average age = $x+4$
New sum of ages = $15(x+4) = 15x+60$
Let $y$ be the average age of 2 new members.
$15x-60-70+2y = 15x+60$
$⇒2y = 60 + 60 +70$
$\therefore y = \frac{190}{2} = 95$
Hence, the correct answer is 95 years.
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