Question

18 men can complete a work in 10 days .16 women can complete a piece of work in 20 days.only 8 men started the work and work for few days .the remaining work was completed by 8 men and 6 women together in 8 8/9 days.for how many days did 8 men only work

Answer 1

18 men---10 days == 1 work
18 men-----1 day === 1/10 work
1 man----- 1 day === 1/180 work

16 women----20 days === 1 work
16 women-----1 day === 1/20 work
1 woman------ 1 day === 1/320 work

8 men in 1 day do: 8/180 = 2/45 work
6 women in 1 day do : 6/320 = 3/160 work
In 1 day they do: 2/45 + 3/160 = 32*2 + 3*9/1440 = 91/1440 work
In 8 8/9 days: 80/9 * 91/1440 = 8*91/9*144 = 91/9*18 = 91/162 work

So the work remaining = 1 - 91/162 = 71/162 work
This work was done by 8 men alone (initially)
8 men:
1day=== 2/45 work
X days=== 71/162 work
2X/45 = 71/162
X = 3195/324 = 355/36 = 9 31/36 days or 9.86 days
Hope it helps.