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### Oliveboard Question of the day

Question: 12 women can complete a work in N days. 7 men can finish the same work in (N+9) days. The time taken by 9 women to complete the work is 2/3 times the time taken by 5 men to complete the work. Find the value of N.

(1) 18
(2) 21
(3) 25
(4) 28
(5) 24

#### Solution posted below. Click on the plus sign to view the solution.

The time taken by 9 women to complete the work is 2/3 times the time taken by 5 men to complete the work.

It means efficiency of 9 women = 3/2 times the efficiency of 5 men

Efficiency of 6 women = Efficiency of 5 men

Let a man do 6k units of work in a day.

Then, a woman does 5k units of work in a day.

12 women can complete the work in N days and 7 men in (N+9) days.

Hence, total work = 12 x 5k x N = 7 x 6k x (N+9)

60kN = 42k(N+9)

60N = 42N + 378

18N = 378

N = 21 days