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