A does a piece of work in 5 more days than B and 9 more days than C. If A & B together can complete the whole work in same time in which C alone does, then in how many days A alone could complete the same work.

15

Let C can finish the work in= x days

ATQ,

A will do it in = (x + 9) days

B will do it in = (x + 9) - 5 = (x + 4) and

If time taken by A + B is same as C i.e. x days, then

⇒ A takes 9 days more than the time taken by A+B and

⇒ B takes 4 days more than the time taken by A+B.

Therefore,

Time taken by A + B = \(\sqrt {9 × 4}\) = \(\sqrt {36}\) = 6 days

Hence,

A alone complete the same work in = 6 + 9 = 15 days