The work done by a woman in 6 h is equal to the work done by a man in 4 h and by a boy in 8 h. Working 8 h per day, if 8 women can complete the work in 10 days, then in how many days can 10 women, 10 men and 10 boys together finish the same work working 8 h per day?

Correct option is B

Given:

The work done by a woman in 6 h is equal to the work done by a man in 4 h and by a boy in 8 h.

Working 8 h per day, 8 women can complete the work in 10 days.

To Find:

In how many days can 10 women, 10 men, and 10 boys together finish the same work working 8 h per day?

Solution:

Let W, M, and B be the amount of work done by a woman, man, and boy in 1 hour, respectively.

From the given information, we have:

6W = 4M = 8B

We can express M and B in terms of W:

M = $$\frac64$$​W = $$\frac 32$$​W

B = $$\frac 68$$​W = $$\frac 34$$​W

Now, let's find the total work done.

8 women working 8 hours per day for 10 days complete the work.

Total work = 8 women × 8 hours/day × 10 days × W

Total work = 640W

Now, let's find the work done by 10 women, 10 men, and 10 boys in 1 hour:

10W + 10M + 10B = 10W + 10$$\times \frac 32\times$$​W + 10$$\times\frac 34\times$$​W

= 10W + 15W + 7.5W

= 32.5W

They work 8 hours per day, so their combined work in 1 day is:

32.5W × 8 hours/day = 260W per day

Let D be the number of days required for them to complete the total work.

Total work = (Work done per day) × Number of days

640W = 260W × D

D = $$\frac{640W }{ 260W}$$​​

D = $$\frac{32 }{13}= 2\frac {6}{13}$$​​

Therefore, 10 women, 10 men, and 10 boys together can finish the same work in $$2\frac {6}{13}$$ days.