Q. The work capacity of A is three times more than that of B. Both of them together can complete a work in 15 days. In how many days will A alone complete that work?

Correct Answer: (B) 20

Explanation:

1. Define Variables:

– Let the work rate of B be r (work units per day).
– Since A’s capacity is three times more than B’s, the work rate of A is 3r.

2. Combined Work Rate:

– Together, A and B have a combined work rate of 3r + r = 4r.

3. Total Work:

– If A and B together complete the work in 15 days, the total work W can be expressed as:
W = Combined Rate × Time = 4r × 15 = 60r

4. Work Rate of A Alone:
– The work rate of A alone is 3r.
– To find the time T A alone takes to complete the work:

T = W / A’s Rate = 60r / 3r = 20 days

Answer: (B) 20