In a group of 150 people, $\frac{2}{5}$ are men , $\frac{1}{3}$ are women and the rest are children. The average of the women is $\frac{4}{5}$ of the average age of the men. The average age of the children is $\frac{1}{5}$ of the average age of the men. If the average age of the men is 50 years, then the average age of all the people in the group is:
Answer & explanation
Correct answer: option 2
Number of man = \(\frac{2}{5}\) × 150 = 60
Number of Women = \(\frac{1}{3}\) × 150 = 50
Number of children = 150 - 60 - 50 = 40
Ratio of average age of women to men = 4 : 5
Ratio of average age of children to men = 1 : 5
Now , Women : Men : Children = 4 : 5 : 1
ATQ , Average age of men = 50
5R = 50
SO , Average age of women = 40 & average age of children = 10
Sum of age of 60 men = 60 × 50 = 3000
Sum of age of women = 50 × 40 = 2000
Sum of age of children = 10 × 40 = 400
Average of all = \(\frac{3000 + 2000 + 400}{5}\)
= \(\frac{5400}{150}\)
= 36