CAT 2023 Slot 2 QA Question & Solution
Question
Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is
Options
Solution
Let the time taken by A to fill the tank alone be x hours, which implies the time taken by B to empty the tank alone is (x-1) hours (B is the drainage pipe), and the time taken by C to fill the tank is y hours.
It is given that when pipes A, B, and C are turned on together, the empty tank is filled in two hours.
Hence, $\frac{1}{x}-\frac{1}{x-1}+\frac{1}{y}=\frac{1}{2}$ .... Eq(1)
It is given that if pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank.
Hence, B worked for 1 hour, and C worked for 2 hours 15 minutes, which is equal to $\frac{9}{4}$ hours.
In 1 hour, B worked $-\frac{1}{x-1}$ units, and in $\frac{9}{4}$ hours, C worked $\frac{9}{4y}$ units.
Hence, $\frac{9}{4y}-\frac{1}{x-1}=1$ .... Eq(2)
Solving both equations, we get $y=\frac{3}{2}$, and $x=3$
Hence, the time taken by C is $\frac{3}{2}$ hours, which is equal to $90$ minutes.
The correct option is A