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?

24.8 days

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