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.
Answer & explanation
Correct answer: option 1
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