8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days. How long will take for 2 women and 1 man to build it together?

Correct option is D

Given:
8 men and 12 women can build a wall in 10 days.
6 men and 8 women can build the same wall in 14 days. 

Formula Used: ​

Total work = Efficiency $$\times$$ time $$\times$$ total worker

Solution: ​

Total work is equal for both the condition So, 

​$$(8M+12W)\times 10 = (6M+8W)\times 14 \\ \ \\ 80M+120W = 84M+112W \\ \ \\ 4M = 8W \\ \ \\ \frac{M}{W} = \frac{2}{1}$$

Now efficiency ratio of men and women = 2 : 1 

So, 

​$$(2W+1M) \times D = (8\times 2+12\times 1)\times 10 \\ \ \\ (2\times 1+1\times2) \times D = (8\times 2+12\times 1)\times 10\\ \ \\ 4 \times D = 28 \times 10 \\ \ \\ D = \frac{28 \times 10}{4} \\ \ \\ D = 70 \ days$$​​