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

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
$$\eqalign{ & = \left( {\frac{{60 \times 24 + 50 \times 30 + 15 \times 66}}{{120}}} \right){\text{ years}} \cr & = \left( {\frac{{3930}}{{120}}} \right){\text{ years}} \cr & = 32.75{\text{ years}} \cr} $$