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?

21\(\frac{49}{54}\) days

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