## Pipes and Cistern

#### Pipes and Cistern

1. A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then third pipe is also opened. In what time is the cistern emptied ?

1. Part filled in 5 min. = 5 x (1/12 + 1/15) = 5 x 9/60 = 3/4

Part emptied in 1 min. (when all the pipes are opened) = 1/6 - (1/12 + 1/15) = (1/6 - 3/20) = 1/60

##### Correct Option: D

Part filled in 5 min. = 5 x (1/12 + 1/15) = 5 x 9/60 = 3/4

Part emptied in 1 min. (when all the pipes are opened) = 1/6 - (1/12 + 1/15) = (1/6 - 3/20) = 1/60

Now, 1/60 part is emptied in 1 min. 3/4 part will be emptied in (60 x 3/4) = 45 min.

1. A leak in the bottom of a tank can empty the full tank in 6 hours. An Inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the Inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank is ?

1. Part filled by intel in 1 hour = (1/6 - 1/8) = 1/24
So, the inlet can fill the tank in 24 hours

##### Correct Option: B

Part filled by inlet in 1 hour = (1/6 - 1/8) = 1/24
So, the inlet can fill the tank in 24 hours
∴ Capacity of the tank = Water that flows in 24 hours = (4 x 24 x 60) liters = 5760 liters

1. Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes ?

1. Let Y be closed after T min
Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1

##### Correct Option: B

Let Y be closed after T min
Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1
⇒ (7 x T)/96 + (18 - T)/24 = 1
or 7T + 72 - 4T = 96.
∴ 3T = 24
or T = 8 min.

1. A water tank is 2/5th full pipe A can fill the tank in 10 minutes and the pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

1. Time taken to fill or empty the whole tank = (6 x 10) /(6 - 10) = - 15 minutes
- ve sign shows that the tank will be emptied.

##### Correct Option: A

Time taken to fill or empty the whole tank = (6 x 10) /(6 - 10) = - 15 minutes
- ve sign shows that the tank will be emptied.

∴ 2/5th full of the tank will be emptied in 15 x 2/5 = 6 minutes

1. Top A can fill a water tank in 25 minutes, tap B can fill the same tank in 40 minutes and tap C can empty the tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied ?

1. Required answer = (25 x 40 x 30) / (40 x 30 + 25 x 30 - 25 x 40)

##### Correct Option: D

Required answer = (25 x 40 x 30) / (40 x 30 + 25 x 30 - 25 x 40)
= 600 / 19 = 3111/19 minutes