a works five times as fast as B and B works five times as fast as C. All three working together can finish the work in 15 days with the help of D. If D alone can finish the work in 60 days, then in how many days will A alone finish the work?
Answer & explanation
Correct answer: option 3
Let the efficiency of D = 1
So, the task in total = 1 × 60 = 60 unit
efficiency of A : B : C
5 : 1
5 : 1
overall ratio of efficiency 25 : 5 : 1
All four finish the work in 15 days, hence
Total work = Efficiency × Number of days
Total work = 1 × 60 = 60
[31x + 1] × 15 = 60
31x + 1 = 4
x = \(\frac{3}{31}\)
A's efficiency = 25 × \(\frac{3}{31}\) = \(\frac{75}{31}\)
A alone can finish the work in = \(\frac{60}{75}\) × 31 = \(\frac{124}{5}\) = 24.8 days