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?
Answer & explanation
Correct answer: option 4
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 days
Working together, time taken = \(\frac{300}{62}\) = \(\frac{150}{31}\)