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.

The work must be finished in 1/4 day.

Concept Used:
The amount of work done by one man, one woman, and one boy in 1 day is given by:

​$$\text{Work by 1 man in 1 day} = \frac{1}{3}\\\ \\\text{Work by 1 woman in 1 day} = \frac{1}{4}\\\ \\\text{Work by 1 boy in 1 day} = \frac{1}{12}$$

Solution:

The total work done by 3 men and 4 women in 1 day is:

​$$3 \times \frac{1}{3} + 4 \times \frac{1}{4} = 1 + 1 = 2$$​​

The total work that must be completed in 1/4 day is:

​$$\text{Work required} = 4 \, \text{units per day}$$​​

The remaining work to be done by boys is:

​$$4 - 2 = 2 \, \text{units}$$​​

Let the number of boys be x .

The work done by x boys in 1 day is:

​$$x \times \frac{1}{12}$$​​

Equating the work done by boys to the remaining work:

​$$x \times \frac{1}{12} = 2\\\ \\x = 2 \times 12 = 24$$​​

Therefore, 24 boys are needed to help 3 men and 4 women finish the work in 1/4 day.