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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?

A. 32.75 yeras B. 38.45 years C. 45.25 years D. 50.5 years Answer: Option A
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Solution(By Apex Team)

Number of men = $\Large\frac{1}{5}$× 120 = 24 Number of women = $\Large\frac{1}{4}$× 120 = 30 Number of children = 120 – (24 + 30) = 66 Average age of men = 60 years Average age of children = $\Large\frac{1}{4}$× 60 = 15 years Average age of women = $\Large\frac{5}{6}$× 60 = 50 years ∴ Avarage age of the group $=\left(\Large\frac{(60\times24+50\times30+15\times66)}{120}\right)\text{years}$ $=\left(\Large\frac{3930}{120}\right)\text{years}$ $=32.75\text{years}$

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