If X works alone, he would take 7 days more to complete the work than if both X & Y worked together, if Y worked alone he would take 28 days more to complete the work than X & Y work together. How many days would they take to complete the work if both of them worked together?

14 days

 Time taken by (X + Y) = P = \(\sqrt {7 × 28 }\) = 14 days

Or

Let X & Y will take 'P' days to complete the work

Now X alone will take = (P + 7) days

Y alone will take = (P + 28) days

\(\frac{1}{P + 7}\) + \(\frac{1}{P + 28}\) =\(\frac{1}{P}\)

\(\frac{2P + 35}{(P + 7) (P + 28)}\) = \(\frac{1}{P}\)

                   2P² + 35P = P² + 35P + 196

                               P² = 196

                               P = 14 days