A tank is filled in 4 hours by three pipes A, B and C. The pipe C is $1\frac{1}{2}$ times as fast as B and B is 3 times as fast as A. How many hours will pipe A alone take to fill the tank?

34

A + B + C = 4 hrs,

Given, The pipe C is 3/2 times as fast as B and B is 3 times as fast as A.

Therefore, A : B : C = 2 : 6 : 9  (Efficiency)

⇒ Total capacity of cistern = (2 + 6 + 9) x 4 = 17 x 4 = 68 units,

⇒ Time taken by A to fill the cistern alone = \(\frac{68}{2}\) = 34 hrs.