Question

12 women can complete a work in 36 days. 18 men in 60 days. 8 men and 20 men work for 20 days. If only men were to comply the work in 4 days. How many men would be required

Answer 1

12 men in 36 days can do a work.

1 man in a day can do 112×36 work.

8 men in 20 days can do 8×2012×36=1027 work.

Similarly, we find that 20 women in 20 days can do 1027work.

Remaining work =727
Now, because in 60 days a work is done by 20 women.

In 1 day a work done by 20×60 women.

In 4 days 727 work is done by 20×60×727×4= 70 women.

Answer 2

12 men can complete a piece of work in 36 days
=> 1 man can complete the work in 36 × 12 days   (∵ less man, more days. inversely proportional)
=> Work done by 1 man in 1 day = 136×12136×12

18 women can complete the same piece of work in 60 days

> 1 woman can complete the work in 60 × 18 days
=> Work done by 1 woman in 1 day = 160×18160×18

Work done by 8 men and 20 women in 1 day = 836×12+2060×18=154+154=127836×12+2060×18=154+154=127

Work done by 8 men and 20 women in 20 days  = 20272027

Remaining work = 1−20271−2027 = 7


Let n women complete this work in 4 days. Then

160×18×n×4=727n15×18=727n=15×18×727=15×2×73=5×2×7=70160×18×n×4=727n15×18=727n=15×18×727=15×2×73=5×2×7=70