Pipes and Cisterns form an important part of the quantitative aptitude section. In the following space, we will see what we mean by inlet pipes or an outlet pipes. We will also see the many types of questions that are present in this section. We will learn about the concept of “leakages” and also note all the important formulae that are necessary for a complete understanding of the section. Let us see more.

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## Outlet Pipes

Let us first state all the important terms and their definitions below:

INLET: A pipe connected with a tank or cistern or a reservoir, that fills it, it is known as Inlet.

OUTLET: A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as Outlet. A pipe can fill a tank in x hours, then: part filled in 1 hour = 1/x.

When a pipe can empty a tank in y hours, then: part emptied in 1 hour = 1/y.

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours( where y>x), then on opening both the pipes, the net part filled in 1 hour=(1/x) – (1/y).

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x>y), then onÂ opening both the pipes, the net part filled in 1 hour= [(1/y) – (1/x)].

Suppose two pipes can fill an empty reservoir in t_{1} and t_{2} min respectively. If both the pipes are opened simultaneously then the time after which the second pipe is closed so that the total time taken to fill the reservoir is T min, is given by (1 + T / t_{1}) t_{2} min.

If there is a hole in a reservoir which empties it in T_{1} hours and a tap is turned on which admits the water in the reservoir at the rate of x litres/hour due to which the reservoir is now emptied in T_{2} hours, then the volume of the reservoir is given by [x (T_{1}Ã—T_{2} / (T_{2} – T_{1}) ] litres.

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## Solved Examples For You

### Part I

Note that a leak is essentially an outlet pipe at the place where it is present. So we will treat it as such.

Example 1: A cistern pump has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?

A) 8 minutesÂ Â Â Â Â Â Â Â B) 10 minutesÂ Â Â Â Â Â Â Â Â Â Â C) 12 minutesÂ Â Â Â Â Â Â Â Â Â Â D) 14 minutes

Answer: Work done by the waste pipe in 1 minute = 1/20 – [1/12 + 1/15] = – 1/10. The negative sign is due to the emptying of the cistern.

Therefore the waste pipe will empty the full cistern in 10 minutes. Hence the correct answer is B) 10 minutes.

Example 2: two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled?

A) 7 hours and 30 minutesÂ Â Â Â Â Â Â Â Â Â Â B) 8 hours and 3 minutesÂ Â Â Â Â Â Â Â Â Â Â Â Â C) 15/2 hours and 1/2 minutesÂ Â Â Â Â Â Â Â Â Â D) None of these are correct and the data is not sufficient.

Answer: Net par filled in 1 hour = [(1/10) + (1/12) – (1/20)]. This can be written as equal to 8/60 or 2/15.

Therefore the tank will be full in 15/2 hours or in other words we may say that 7 hours and 30 minutes. Hence the correct answer here is A) 7 hours and 30 minutes.

### Part II

Example 3: Two pipes A and B can fill a tank in 36 min and 45 min respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. In how much time, the tank is full?

A) 36 minÂ Â Â Â Â Â Â Â B) 46 minÂ Â Â Â Â Â Â Â Â Â Â Â Â C) 56 minÂ Â Â Â Â Â Â Â Â Â Â Â D) 18 min

Answer: Part filled in 7 min = 7[(1/36)+ (1/45)] = 7/20.

Remaining part = [1 – (7/20)] = 13/20

The net part filled in 1 min when A, B and C are open is equal to = [(1/36) + (1/45) – (1/30)] = 1/60.

Now, 1/60 part is filled in 1 min. 13/20 part is filled in [(60Ã—(13/20)] = 39 mi

Total time taken to fill the tank = (39 + 7) min = 46 min. Hence the correct option is B) 46 min.

Example 4: Two pipes A and B can fill a tank in 24 min and 32 min respectively. If both the pipes are open simultaneously, then after how much time B should close so that the tank is full in 18 minutes?

A) 2 minÂ Â Â Â Â Â Â Â Â Â B) 4 minÂ Â Â Â Â Â Â Â Â Â C) 6 minÂ Â Â Â Â Â Â Â Â Â Â D) 8 min

Answer: Let B close after ‘x’ min. Then, we can say that part filled by (A+B) in x min + the part filled by A in (18 – x) min = 1

Therefore, x[(1/24) + (1/32)] + (18 – x) (1/24) = 1.

In other words, we may write: 7x/96 + (18-x)/24 = 1

Or 7x + 4(18 – x) = 96 and this will give x = 8.

Hence, B must close after 8 minutes and the correct answer is D) 8 minutes.

## Practice Questions

Q 1: Two pipes A and B can fill a tank in 20 and 30 min respectively. If both the pipes are used together, then how long will it take to fill the tank?

A) 12 minÂ Â Â Â Â Â Â Â Â Â Â Â B) 15 minÂ Â Â Â Â Â Â Â Â Â Â C) 25 minÂ Â Â Â Â Â Â Â Â Â Â Â D) 50 min

Ans:Â A) 12 min

Q 2: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are open simultaneously, then after how much time will the cistern get filled?

A) 4.5 hoursÂ Â Â Â Â Â Â Â B) 5 hoursÂ Â Â Â Â Â Â Â Â Â C) 6.5 hoursÂ Â Â Â Â Â Â Â Â Â Â D) 7.2 hours

Ans:Â D) 7.2 hours

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