P works thrice as fast as Q and Q works thrice as fast as R. all three working together can finish the task in 7 days with the help of S. If S alone can finish the work in 13 days, then in how many days will P alone finish the task?
Answer & explanation
Correct answer: option 1
Let the efficiency of S = 1
So, the total work = 1 × 13 = 13 unit
efficiency P : Q : R
3 : 1
3 : 1
overall ratio of efficiency 9 : 3 : 1
All four can complete the task in 7 days
Total work = efficiency × Number of days
[9x + 3x + x +1] × 7 = 13
(13x + 1) × 7 = 13
91 x + 7 = 13
x = \(\frac{6}{91}\)
P's efficiency = \(\frac{9 × 6}{91}\) = \(\frac{54}{91}\)
P alone can finish the work in = \(\frac{13}{54}\) × 91 = \(\frac{1183}{54}\)
= 21\(\frac{49}{54}\) days