14 men can complete a piece of work in 6 days, while 20 women can complete the same work in 8 days. 7 men started working on the job, and after working for 3 days all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 6 days?

Correct option is A

Given:

14 men can complete a work in 6days

20 women can complete the same work in 8days

Formula Used:

Work done = Number of workers \times Time

Solution:

Let the efficiency of a man and a woman be M and W respectively.

According to the question,

One day work of one man =$$\frac{1}{14 \times 6} = \frac{1}{84}$$​​

So 3 days’s work of 7 men =$$7 \times 3 \times \frac{1}{84} =\frac{1}{4}$$​​

Remaining work = $$1 -\frac{1}{4} =\frac{3}{4}$$​​

One day work of a woman =$$\frac{1}{20 \times 8} = \frac{1}{160}$$​​

Total work to be completed in 6 days.

Let the women reqiured to complete the work in 6 days be x

Then

​$$6 \times x \times \frac{1}{160} = \frac{3}{4}$$​​

​$$x= \frac{160 \times 3}{6\times 4}$$​

= 20