X completes a piece of work in 12 days, whereas Y completes the same work in 16 days. P is \(1\frac{1}{2}\) times as fast as X. In how many days can Y and P together complete the work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(5\frac{1}{3}\) days
Time is inversely proportional to speed of working: a person \(1\frac{1}{2}\) times as fast takes \(\frac{2}{3}\) of the time.
P alone takes \(\displaystyle 12\times\frac{2}{3}=8\) days
One-day work of Y and P \(\displaystyle =\frac{1}{16}+\frac{1}{8}=\frac{1+2}{16}=\frac{3}{16}\)
Time together \(\displaystyle =\frac{16}{3}=5\frac{1}{3}\) days
Y and P together complete the work in \(5\frac{1}{3}\) days.