Pipe and Cistern

In this article, we will Discuss imporant questions on Pipes and Cistern

Example 1:  A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together, a full tank is emptied in 2 hours. If a bucket can hold 5 liters of water, what is the capacity of the tank?

a.) 120 liters

b.) 240 liters

c.) 180 liters

d.) 60 liters

Solution:  A fills 4 buckets in 24 minutes. Thus, A fills 1 bucket in 24/4 = 6 minutes

Similarly, B fills 8 buckets in 1 hour. Thus B fills 1 bucket in 60/8 minutes

Similarly, C fills one bucket in 20/2 = 10 minutes

In 2 hours,

Number of buckets filled by A will be = 120/6 = 20 buckets

Number of buckets filled by B will be = 120/ (60/8) = (120 * 8) / 60  = 16 buckets

Number of buckets filled by C will be = 120 / 10 = 12 buckets

Total number of buckets filled = (20 + 16 + 12) = 48 buckets

Total amount of water coming out of the tank = capacity of the tank = 48 * 5 liters = 240 liters

Answer Choice: B

Example 2:  There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admit 6 liters per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

a.) 8.8 liters

b.) 36 liters

c.) 144 liters

d.) Cannot be determined

Solution:  Since the leak can empty the tank in 8 hours,

In one hour, part of the tank emptied by the leak = 1/8

Also, after opening the tap, in one hour, part of the tank emptied = 1/12

Let the tap can fill the tank in x hours. Therefore, In one hour, part of the tank filled by the tap = 1/x

As per question, (1/x) – (1/8) = 1/12

Or x = 24

Since the tap admits 6 liters of water per hour, it will admit (6*24) =144 liters of water in 24 hours, which should be the capacity of the tank.

Correct Answer: 24 minutes

Example 3:  Three small pumps and one large pump are filling a tank. Each of the three small pump works at 2/3 of the rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

a.) 4/7

b.) 1/3

c.) 2/3

d.) ¾

Solution:  As per the question,

Let the work done by the big pump in one hour be 3 units. 
Therefore, work done by each of the small pumps in one hour = 2 units. 
Let the total work to be done in filling the tank be 9 units. 
Therefore, time taken by the big pump if it operates alone = 9/3 = 3 hours. 
If all the pumps operate together, the work done in one hour = 3 + 2*3 = 9 units.
 Together, all of them can fill the in 1 hour. Required ratio = 1/3

Answer Choice b

Example 4: 

A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?
1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

Assume the capacity of tank= LCM(6,8)=24units
Inlet pipe can fill 24/8= 3 units every hour.
Outlet pipe can discharge 24/6= 4 units every hour.

Total number of inlet pipes=x
Total number of outlet pipes= 8-x

{(8-x)*4 - 3x}*6= 24
32-4x-3x= 4
x=4

Total number of inlet pipes=4

The correct answer is Choice (1).

Example 5:  Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

a.) 2 hours 30 minutes

b.) 5 hours

c.) 4 hours

d.) 10 hours

Pipe A fills the tank normally in 2 hours.

Therefore, it will fill 1/2 of the tank in an hour.

Let the leak take x hours to empty a full tank when pipe A is shut.

Therefore, the leak will empty 1/x of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak =   (1/2 – 1/x) of the tank. —– (1)

Now, when there is a leak, the problem states that it takes two and a half hours to fill the tank. i.e. 5/2hours.

Therefore, in an hour, 2/5th of the tank gets filled. —– (2)

Equating (1) and (2), we get 1/2 – 1/x = 2/5

=> 1/x = 1/2 – 2/5 = 1/10

=> x = 10 hours.

The correct answer is Choice (4).