If P works alone, he would take 5 days more to complete the work than if P & Q worked together, if Q worked alone, he would take 20 days more to complete the job than P and Q work together. How many days would they take to complete the work if both of them worked together?

10 days

Time taken by (X + Y) = P = \(\sqrt {5 × 20}\) = 10 days

Or

Let P & Q will finish the work in d days

Hence P will take = (d + 5) days

Q will take = (d + 20) days

\(\frac{1}{(d + 5)}\) + \(\frac{1}{(d + 20)}\) = \(\frac{1}{d}\)

\(\frac{d + 20 + d + 5}{(d+ 5) (d + 20)}\) = \(\frac{1}{d}\)

2d² + 25d = d² + 25d + 100

            d² = 100

            d = 10 days