P, Q and R can complete a task together in 15 days. P and R can complete the task together in 40 days. In how many days can Q complete the task alone?

Let's assume the total work is 600 units. (LCM of 15 and 40)

P, Q and R can complete a task together in 15 days.

Efficiency of P, Q and R together = $$\frac{600}{15}$$ = 40 units/day    Eq.(i)

P and R can complete the task together in 40 days.

Efficiency of P and R together = $$\frac{600}{40}$$ = 15 units/day    Eq.(ii)

Efficiency of Q = Eq.(i)-Eq.(ii) = 40-15 = 25 units/day

Time taken by Q alone to complete the task = $$\frac{600}{25}$$

= 24 days