A can finish a work in 16 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work can they finish in a day?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{3}{16}\)
A person who finishes a work in \(n\) days does \(\frac{1}{n}\) of it in one day. Working together, their one-day parts add up.
B takes half of A’s time: \(\frac{16}{2}=8\) days
A’s one-day work \(=\frac{1}{16}\), B’s one-day work \(=\frac{1}{8}\)
Together in one day \(\displaystyle =\frac{1}{16}+\frac{2}{16}=\frac{3}{16}\) of the work