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

Step-by-step explanation:

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

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

x

1

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

y

1

Now,

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

x

2

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

y

5

Then according to the question,

x

2

+

y

5

=

4

1

… (i)

x

1

+

y

1

=

12

1

… (ii)

Multiplying equation (ii) by 5, we get

x

5

+

y

5

=

12

5

... (iii)

Subtracting equation (i) from (iii), we get

x

3

=

12

5

−

4

1

⇒

x

3

=

12

5−3

⇒

x

3

=

12

2

=

6

1

⇒x=18

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

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