If A completes a work in \(x\) days and B does the same work in \(y\) days, in how many days will A and B together complete that work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{x y}{x+y}\) days
Work done in one day is the reciprocal of the days needed for the whole work, and when two people work together their one-day works add.
A’s one-day work \(\displaystyle =\frac{1}{x}\); B’s one-day work \(\displaystyle =\frac{1}{y}\)
Together in one day: \(\displaystyle \frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\)
Days for the whole work \(\displaystyle =\frac{xy}{x+y}\)