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?
Answer & explanation
Correct answer: option 3
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