Correct Answer - Option 3 : 25 days
Given:
15 men and 10 women complete a piece of work in 30 days
The same piece of work is completed by 10 men and 20 women in 20 days
Formula used:
Work = Time × Efficiency
Calculation:
Let the efficiency of a man be M
And the efficiency of a woman be W
Now, using the first given condition
⇒ Total work = (15M + 10W) × 30
⇒ Total work = 450M + 300W ----(1)
Use the second given condition
⇒ Total work = (10M + 20W) × 20
⇒ Total work = 200M + 400W ----(2)
By equating equation (1) and (2) we get
⇒ 450W + 300W = 200M + 400W
⇒ 450M - 200M = 400W - 300W
⇒ 250M = 100W
⇒ M/W = 100/250
So, the ratio of efficiency of man and woman is 2 : 5
⇒ Time work = 200 × 2 + 400 × 5
⇒ Time work = 2400
One-third of the total work
⇒ 2400/3 = 800
Total efficiency of 6 men and 4 women
⇒ 6 × 2 + 4 × 5
⇒ 12 + 20 = 32
⇒ Time = 800/32 = 25 days
∴ 6 men and 4 women will complete the one-third of the work in 25 days
