In a group of 120 people, one-fifth are men, one-fourth are women and the rest children. The average age of women is five-sixth of the average age of men. Average age of children is one-fourth of the average age of men. If average age of men is 60 years, what is the average age of the group?

Answer: Option A

Number of men
= $$\frac{1}{5}$$ × 120
= 24
Number of women
= $$\frac{1}{4}$$ × 120
= 30
Number of children
= 120 - (24 + 30)
= 66
Average age of men = 60 years
Average age of children
= $$\frac{1}{4}$$ × 60
= 15 years
Average age of women
= $$\frac{5}{6}$$ × 60
= 50 years
∴ Avarage age of the group
$$\begin{array}{rl}& =\left(\frac{60\times 24+50\times 30+15\times 66}{120}\right)\text{ years}\\ & =\left(\frac{3930}{120}\right)\text{ years}\\ & =32.75\text{ years}\end{array}$$