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.
Solution
6 men + 6 women can finish the work in = 24 days
144 men + 144 women can finish it in = 1 day
8 m + 12 women can finish the work in = 15 days
120 men + 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 1/2` women
(ii) In first case,
`6xx3/2+6=9+6`
= 15 women
In second case,
`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
and 12 women will do it in
=`(24xx15)/12`
= 30 days
