Correct Answer - Option 2 : 66 days
Given:
A piece of work is completed by 3 men and 4 boys in 7 days.
The same piece of work is completed by 5 men and 3 boys in 6 days
Formula used:
Work = Time × Efficiency
Calculation:
Let the efficiency of a man be M
And the efficiency of a boys be B
Now, using the first given condition
⇒ Total work = (3M + 4B) × 7
⇒ Total work = 21M + 28B ----(1)
Use the second given condition
⇒ Total work = (5M + 3W) × 6
⇒ Total work = 30M + 18W ----(2)
By equating equation (1) and (2) we get
⇒ 21M + 28B = 30M + 18W
⇒ 30M - 21M = 28B - 18W
⇒ 9M = 10B
⇒ M/B = 10/9
So, the ratio of efficiency of man and boy is 10 : 9
⇒ Time work = 21 × 10 + 28 × 9
⇒ Time work = 462
Four times of the total work is
⇒ 462 × 4 = 1848
The total efficiency of 1 man and 2 boys
⇒ 1 × 10 + 2 × 9
⇒ 10 + 18 = 28
⇒ Time = 1848/28 = 66 days
∴ 1 man and 2 boys will complete the four times of the same work in 66 days.
