A tank is filled in 4 hours by three pipes A, B, and C. Pipe C is twice as fast as pipe B, and pipe B is twice as fast as pipe A. How much time will pipe A take to fill the tank?

Correct option is B

Given:

Three pipes A, B, and C fill the tank together in 4 hours.
Pipe C is twice as fast as pipe B.
Pipe B is twice as fast as pipe A.

Solution:

Let the rate of pipe A be x (in terms of tank capacity per hour).
Thus, pipe B’s rate will be 2x, and pipe C’s rate will be 4x.
Combined rate of A, B, and C = x + 2x + 4x = 7x
Since the tank is filled in 4 hours, the combined rate is 1/4 (since the tank is filled in 4 hours).
Thus, we have the equation:
​$$7x = \frac{1}{4} \\\ \\x = \frac{1}{28}$$​​
The rate of pipe A is $$\frac{1}{28}$$​, so the time taken by pipe A to fill the tank is:
Time = $$\frac{1 }{ (\frac{1}{28})}$$​ = 28 hours
Thus, pipe A will take 28 hours to fill the tank by itself.