8 men and 6 women can complete a piece of work in 5 days while 6 men and 8 women can also complete the same work in 5 days. In how many days will 7 men and 7 women complete the same work?

Correct option is D

Given :

8 men and 6 women can complete a piece of work in 5 days.

6 men and 8 women can also complete the same work in 5 days. 

Concept Used: ​

Total work =  Efficiency $$\times$$ Number of men/women $$\times$$​  Total time 

Solution : 

Let the efficiency of men is m and efficiency of women is w

According to the question,

​$$(8m+ 6w)5 = 5(6m + 8 w) \\ \ \\ 8m + 6w = 6m+8w \\ \ \\ 8m-6m = 8w-6w \\ \ \\ 2m = 2w \\ \ \\ \frac{m}{w} = \frac{1}{1}$$ 

Now, 

(7w + 7m)D = 5(8m + 6w) 

(7(1) + 7(1))D = 5(8(1) + 6(1))

14 $$\times$$​ D = 5 $$\times$$ 14

D = 5 

Thus, 7 men and 7 women complete the same work in 5 days.