P alone can do \(\frac{3}{5}\) of a work in 15 days. Q is 25% more efficient than P. R alone can do the same work in 5 days less than Q. S is 25% less efficient than R. If they all work together, then the work will be completed in how many days?

\(\frac{150}{31}\) days

Total time of P = \(\frac{5}{3}\) x 15 = 25 days

               P       :      Q

Eff.   →    4       :       5         (@25% more)

Time →   5       :       4

              ↓ × 5          ↓ × 5

             25 days     20 days

Time taken by R = 20 - 5 = 15 days

               R       :      S

Eff.   →    4       :       3         (@25% less)

Time →   3       :       4

              ↓ × 5          ↓ × 5

             15 days     20 daysWorking together, time taken = \(\frac{300}{62}\) = \(\frac{150}{31}\)