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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 t
Question

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.

A.

3 : 4

B.

2 : 1

C.

1 : 2

D.

4 : 3

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)×4=(12m+18w)×2 20m+12w=12m+18w 20m12m=18w12w 8m=6w mw=68=34(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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