P works thrice as fast as Q, and Q works thrice as fast as R. P, Q and R together, with the help of S, can finish a task in 7 days. If S alone can finish the task in 13 days, in how many days can P alone finish it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(21\frac{49}{54}\) days
Take R's daily work as \(r\); then Q does \(3r\) and P does \(9r\), so P, Q and R together do \(13r\) a day. Taking away S's share from the four together gives \(13r\).
All four together do \(\frac{1}{7}\) of the task per day; S alone does \(\frac{1}{13}\)
\(\displaystyle 13r=\frac{1}{7}-\frac{1}{13}=\frac{13-7}{91}=\frac{6}{91}\), so \(\displaystyle r=\frac{6}{1183}\)
P does \(\displaystyle 9r=\frac{54}{1183}\) of the task per day
P alone takes \(\displaystyle \frac{1183}{54}=21\frac{49}{54}\) days