Question

12) In a group of 120 members, one fifth are adult men, one-fourth are adult women and the rest
are children. The average age of women is five-sixth of the average age of men. The average
age of children is one-fourth of the average age of men. If the average age of, men is 60
years, then the average age of 120 members is?
a) 35
b) 32.75
c) 38
d) 36.2​

Answer 1

Answer:

32.75

Step-by-step explanation:

$the \: \frac{1}{5} \: are \: men \: = \frac{1}{5} \times 120 = 24 \\ the \: \frac{1}{4} are \: women = \frac{1}{4} \times 120 = 30 \\ rest \: are \: child = 120 - 24 - 30 = 66 \\ avg \: age \: of \: women \: = \: \frac{5}{6} avg \: of men \: \\ = \frac{5}{6} \times 60 = 50 \\ avg \: age \: of \: child = \frac{1}{4} avg \: of \: men = \\ \frac{1}{4} \times 60 = 15 \\ avg \: age\: of \: men \: = 60 \\ all \: avg \: age \: = \frac{(24 \times 60) + (30 \times 50) + (66 \times 15)}{120} \\ = \frac{1440 + 1500 + 990}{120} \\ = \frac{3930}{120} \\ = 32.75$