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 50 days to complete the same work. then Q alone can do it in Options.
A) 30 days B) 25 days C) 20 days D) 15 days E) 24 days

Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 50 work done by p , q and r in 1 day = 1 / 10 + 1 / 50 = 6 / 50 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 × 2 = 6 / 50 = > work done by p in 1 day = 3 / 50 = > work done by q and r in 1 day = 3 / 50 hence work done by q in 1 day = 3 / 50 – 1 / 50 = 2 / 50 = 1 / 25 so q alone can do the work in 25 days option b"
Answer: B