Question

If 4 men or 6 women can finish a piece of work in 20 days then in how many days can 6 men and 11 women finish the same work

Answer 1

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Answer 2

6 men and 11 women finish the same work in 6 days.

First we have to find the work rate of the man (work/day)

4 men takes 20 days to finish the work

So, 1 man takes (40 × 2) days = 80 days to finish the work

So, work rate of 1 man = 1/80.

Similarly, work rate of 6 men = 6 × (1/80) = 6/80         ...(1)

Similarly, 6 women also takes 20 days to finish the same work.

So, 1 woman will take (60 × 2) days = 120 days to finish the work

So, work rate of 1 woman = 1/120.

Similarly, work rate of 11 women = 11 × (1/120) = 11/120     ...(2)

Thus the combined work rate of 6 men and 11 women is:       [Addition of (1) and (2)]

(6/80) + (11/120) =  40/240 = 1/6

Total no. of days taken = (Work rate)⁻¹ = (1/6)⁻¹ days = 6 days.

So, 6 days taken.