10 men and 6 women can do a piece of work in 4 days, whereas 12 men and 18 women can do it in 2 days. Find the ratio of the daily work done by a man to that done by a woman, respectively.

Correct option is A

Given:

10 men and 6 women can complete the work in 4 days.

12 men and 18 women can complete the work in 2 days.

We need to find the ratio of the daily work done by a man to that done by a woman 

Formula Used: 

Total Work = Efficiency $$\times$$ time​

Solution:

Let the daily work done by a man be m and the daily work done by a woman be w

Now, 

​$$(10m+6w)\times4 = (12m+18w)\times 2 \\ \ \\ 20m+12w = 12m+18w \\ \ \\ 20m-12m = 18w-12w \\ \ \\ 8m = 6w \\ \ \\ \frac m w = \frac 6 8 = \frac 34$$​​

The ratio of the daily work done by a man to that done by a woman is 3 : 4 

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