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. The average age of these two women is

• A. 52 years
• B. 56 years
• C. 48 years
• D. 44 years

Answer 1

The Correct Option is C

The total increase in age for the group is
\(\Rightarrow \;\)\(8 \times 2 = 16 \, \text{years}\)
The total age of the two men is
\(\Rightarrow \;\)\(35 + 45 = 80 \, \text{years}\)
Let the total age of the two women be \(x\). 
\(\therefore\) The increase in total age is 
\(\Rightarrow \;\)\(x - 80 = 16\)
\(\Rightarrow \;\)\(x = 80 + 16 = 96\)
The average age of the two women is:
\(\Rightarrow \;\)\(\frac{96}{2} = 48 \, \text{years}\)

Hence, the average age of the two women is 48 years.