P works twice as fast as Q, and Q works twice as fast as R. P, Q and R together, with the help of S, can finish a task in 6 days. If S alone can finish the task in 14 days, in how many days can P alone finish it?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(18\frac{3}{8}\) days
Take R's daily work as \(r\); then Q does \(2r\) and P does \(4r\), so P, Q and R together do \(7r\) a day. Taking away S's share from the four together gives \(7r\).
All four together do \(\frac{1}{6}\) of the task per day; S alone does \(\frac{1}{14}\)
\(\displaystyle 7r=\frac{1}{6}-\frac{1}{14}=\frac{7-3}{42}=\frac{2}{21}\), so \(\displaystyle r=\frac{2}{147}\)
P does \(\displaystyle 4r=\frac{8}{147}\) of the task per day
P alone takes \(\displaystyle \frac{147}{8}=18\frac{3}{8}\) days