Correct Answer - Option 3 : 4 days
Formula used:
M1 × D1 = M2 × D2
Here M is any person, who is doing the work and D is the time taken to do the work
Concept used:
Here M1 and M2 is the efficiency of the person who is doing the work
Calculation:
Let the required time taken be y days
For notation, Men = M and Boy = B
M1 × D1 = M2 × D2
⇒ (16M + 12B) × 5 = (24M + 13B) × 4 = (16M + 17B) × y
Taking the first two equations
⇒ (16M + 12B) × 5 = (24M + 13B) × 4
⇒ 80M + 60B = 96M + 52B
⇒ 8B = 16M
⇒ B = 2M
Taking the last two equations
⇒ (24M + 13B) × 4 = (16M + 17B) × y
⇒ 96M + 52B = (16M + 17B) × y
⇒ 96M + 104M = (16M + 34M) × y
⇒ 200M = 50M × y
⇒ y = 4
∴ Required time taken to do the work is 4 days