CAT 2023 Slot 2 Solved Paper

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, ‌

1

x

−‌

1

x−1

+‌

1

y

=‌

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 ‌

9

4

hours.
In 1 hour, B worked −‌

1

x−1

units, and in ‌

9

4

hours, C worked ‌

9

4y

units.
Hence, ‌

9

4y

−‌

1

x−1

=1.....Eq(2)
Solving both equations, we get y=‌

3

2

, and x=3
Hence, the time taken by C is ‌

3

2

hours, which is equal to 90 minutes.
The correct option is A