Question

2 men and 5 women can do a piece of work in 4 days, while one man and one woman
can finish it in 12 days. How long would it take for 1 man to do the work?​

Answer 1

Answer:

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Step-by-step explanation:

1 M + 1 W = 12 days

5M + 5W = 12/5 = 2.4 days……(1)

2M + 5W = 4 days…….(2)

Subtracting (2) from (1) we get:

3M = (2.4 * 4) / (4 - 2.4) = 9.6/1.6 = 6

1M = 3*6 = 18 days

NOTE:

If (A+B) and B can complete a piece of work in x days and y days respectively, then A alone can do it in (x*y)/(y-x) days

Answer 2

Answer:

18

Step-by-step explanation:

Let’s assume that 1 man takes x days to do work and y days for a women.

So, the amount of work done by 1 man in 1 day = 1/x

And the amount of work done by 1 woman in 1 day = 1/y

Now,

The amount of work done by 2 men in 1 day will be = 2/x

And the amount of work done by 5 women in 1 day = 5/y

Then according to the given conditions in the problem, we have

2/x + 5/y = ¼ … (i)

1/x + 1/y = 1/12 … (ii)

Multiplying equation (ii) by 5, we get

5/x + 5/y = 5/12

2/x + 5/y = ¼

(-)—(-)—(-)

3/x = 5/12 – ¼

3/x = (5 – 3)/12

3/x = 2/12 = 1/6

x = 18

Therefore, 1 man can do the work in 18 days.