Time and work Quantitative aptitude question

[Q] 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(a) 60 days
(b) 40 days
(c) 50 days
(d) 30 days

Solution

Answer   (b)
Explanation
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Work done by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as

4m + 6w = 1/8 ---(1)

3m + 7w = 1/10 ---(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

Ie, 10 women can complete the work in 40 days