Question

A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days. Find :
(i) according to the amount of work done, one man is equivalent to how many women.
(ii) the time is taken by 4 men and 6 women to complete the same work.

Answer 1

6 men and 6 women can finish the work in 24 days

∴ 144 men and 144 women can finish it in 1 day

8 men and 12 women can finish the work in 15 days

∴ 120 men and 180 women can finish it in 1 day

(i) 144 men + 144 women = 120 men + 180 women

⇒ 144 men – 120 men = 180 women – 144 women

⇒ 24 men = 36 women

1 man =`36/24`

`=3/2` women

1 man `=1 1/2` women

(ii) In the first case, 6 men and 6 women are equivalent to

= `6xx3/2+6`

= 9+6

= 15 women

In the second case, 4 men and 6 women are equivalent to 

`4xx3/2+6`

= 6 + 6

= 12 women

Now, 15 women can do a piece of work in = 24 days

1 women will do it in =  24 × 15 days 

12 women will do it in = `(24xx15)/12`

= 30 days

4 men and 6 women will do the same work in 30 days.