P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 20 days to complete the same work. then Q alone can do it in  Choose the correct choice from the following choices:
A) 20
B) 22
C) 25
D) 27
E) 40

Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 20 work done by p , q and r in 1 day = 1 / 10 + 1 / 20 = 3 / 20 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 3 / 20 = > work done by p in 1 day = 3 / 40 = > work done by q and r in 1 day = 3 / 40 hence work done by q in 1 day = 3 / 40 â € “ 1 / 20 = 1 / 40 so q alone can do the work in 40 days answer is e ."
Answer: E