A man, a woman and a boy can do a work individually in 3, 4 and 12 days respectively. How many boys are to be employed to help 3 men and 4 women to finish the work in 1/4 of a day?

Correct option is C

Given:

A man can complete the work in 3 days.
A woman can complete the work in 4 days.
A boy can complete the work in 12 days.
Solution:

A man, a woman and a boy can do a work individually in 3, 4 and 12 days respectively.

LCM of 3, 4 and 12 = 12
Efficiency of man = 12/3 = 4 unit/day
Efficiency of women = 12/4 = 3 unit/day
Efficiency of boys = 12/12 1 unit/day
Total days = 12/8
As we know,
Work = efficiency × time
3 men = 3 × 4 =12
4 women = 4 × 3 = 12
Let x boys are required with 3 men and 4 women to complete the work in ¼ days
Then
​$$12×\frac{1}{4}+12×\frac{1}{4}+x×\frac{1}{4} = 12 \\\\ \\3 + 3 + x×\frac{1}{4 }= 12 \\\ \\x×\frac{1}{4}=6 \\\ \\x = 24$$​​