Correct Answer - Option 2 : 50/3 days
Given:
7 men and 3 women complete a piece of work in 10 days
The same piece of work is completed by 6 men and 9 women in 5 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 = (7M + 3W) × 10
⇒ Total work = 70M + 30W ----(1)
Use the second given condition
⇒ Total work = (6M + 9W) × 5
⇒ Total work = 30M + 45W ----(2)
By equating equation (1) and (2) we get
⇒ 70W + 30W = 30M + 45W
⇒ 70M - 30M = 45W - 30W
⇒ 60M = 15W
⇒ M/W = 15/40
So, the ratio of efficiency of man and woman is 3 : 8
⇒ Time work = 70 × 3 + 30 × 8
⇒ Time work = 450
Total efficiency of 1 men and 3 women
⇒ 1 × 3 + 3 × 8
⇒ 3 + 24 = 27
⇒ Time = 450/27 = 50/3 days
∴ 1 men and 3 women will complete the work in 50/3 days
