2 men can complete a piece of work in 15 days while 5 women can do it in 14 days. In how many days can 7 women and 3 men complete it?

Correct option is C

Given:

2 men can complete the work in 15 days.

5 women can complete the work in 14 days.

To find: In how many days can 7 women and 3 men complete the work?

Formula Used:

Work done = (Number of people) × (Rate of work) × (Time taken)

Time taken = $$\frac{1}{\text{Rate of work}}$$​

Solution:

Rate of work of 1 man:

2 men complete the work in 15 days, so the rate of work of 2 men is $$\frac{1}{15}$$ of the work per day.

Rate of work of 1 man =$$\frac{1}{15} \times \frac{1}{2} = \frac{1}{30}$$ of the work per day.

Rate of work of 1 woman:

5 women complete the work in 14 days, so the rate of work of 5 women is $$\frac{1}{14}$$ of the work per day.

Rate of work of 1 woman $$= \frac{1}{14} \times \frac{1}{5} = \frac{1}{70}$$​ of the work per day.

Rate of work of 7 women and 3 men:

Rate of work of 7 women $$= 7 \times \frac{1}{70} = \frac{7}{70} = \frac{1}{10}$$​​

Rate of work of 3 men = $$3 \times \frac{1}{30} = \frac{3}{30} = \frac{1}{10}$$​​

Total rate of work $$= \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5}$$​​

Time taken for 7 women and 3 men to complete the work:

Time taken = $$\frac{1}{\text{Rate of work}} = \frac{1}{\frac{1}{5}}$$​= 5 days.

7 women and 3 men can complete the work in 5 days.