Question

In a group of 150 people, 2/5 are men, 1/3 are women and the rest are children. The average age of the women is 4/5 of the average age of the men. The average age of the children is 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?

• A. 35 years
• B. 32 years
• C. 28 years
• D. 36 years

Answer 1

Answer:

D. 36 years

Solution:

Given:

Total people = 150

Average age of men = 50 years

Formula used:

Average = Sum of values/Number of values

Calculation:

Total men in the group $=\frac{2}{5}\times{150} = 60$

Total women in the group $=\frac{1}{3}\times{150} = 50$

Total children in the group = 150 – 60 – 50 = 40

Average age of men = 50 (given)

Average age of women $=\frac{4}{5}\times{50} = 40$

Average age of children $=\frac{1}{5}\times{50} = 10$

Now, Total age of men in the group $= 60\times{50} = 3000$

Total age of women in the group $= 50\times{40} = 2000$

Total age of children in the group $= 40\times{10} = 400$

Total age of all persons in the group = 3000 + 2000 + 400 = 5400

Average age of persons in the group $=\frac{ 5400}{150} = 36$

∴ The average age of all the people in the group is 36