# PIPES AND CISTERNS SHORTCUTS

## About the topic pipes and cisterns shortcuts

Pipes and cisterns shortcuts play a major role quantitative aptitude test. There is no competitive exam without the questions from this topic. We have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

Points to remember

 1. If a pipe can fill a tank in ‘m’ hours, it can fill (1/m) part of the tank in 1 hour. 2. If (1/m) part of the tank is filled by a pipe in 1 hour, time taken by the pipe to fill the entire tank is "m" hours. 3. If a pipe can emty a tank in ‘x’ hours, it can empty (1/x) part of the tank in 1 hour. 4. If (1/m) part of the tank is emptied by a pipe in 1 hour, time taken by the pipe to empty the entire tank is "x" hours 5. If a pipe can fill a tank in "x" hours and another pipe can empty the full tank in "y" hours (x>y), then on opening both the pipes, the net part emptied in 1 hour = (1/y - 1/x)

## Why do students have to study this topic?

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from this topic. To solve problems in this topic, students must be knowing pipes and cisterns shortcuts. Whether a person is going to write placement exam to get placed or a students is going to write a competitive exam in order to get admission in university, they must be prepared to solve time and work problems. This is the reason for why people must study this topic. ## Benefit of studying this topic

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

## How can students do problems on pipes and cisterns?

To solve problems on pipes and cisterns easily and quickly, they have pipes and cisterns shortcuts. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to do the problems which are being asked from this topic in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time.

## Shortcuts we use to solve the problems

Pipes and cisterns shortcuts are nothing but the easiest way to solve problems related to pipes and cisterns. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some problems on pipes and cisterns . You can check your answer online and see step by step solution.

1. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

 (A) 6 min. to empty (B) 7 min. to empty (C) 6 min. to full (D) 7 min. to full

jQuery UI Accordion - Default functionality
From the question, we have to consider an important thing.
That is, pipe B is faster than pipe A.
When two pipes are opened together, the tank will emptied.
So the right choice would be (A) or (B)

Total capacity of the tank = 60 units. (L.C.M of 10,6)
The tank is already two-fifth full.
That is,quantity of water is in the tank =(2/5)X60 = 24 units
If both the pipes are opened together, this 24 units will be emptied.

work done by pipe A = 60/10 = 6 units/min
work done by pipe B = 60/6 = -12 units/min (emptying the tank)

Adding the above two equations, we get(A+B)=-4 units/min
That is 4 units will be emptied per minute when both the pipes are opened together
Time taken to empty 24 units (2/5 of the tank)= 24/4=6 min

Time taken to empty the tank is 6 min. Option (A) is correct.

2. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

 (A) 5.5 hrs (B) 6.5 hrs (C) 7.5 hrs (D) 8.5 hrs

jQuery UI Accordion - Default functionality
Total work = 60 units. (L.C.M of 10,15,20)

work done by the pipe A = 60/10 = 6 units/hr
work done by the pipe B = 60/15 = 4 units/hr
work done by the pipe C = 60/20 = 3 units/hr

(Given:A is open all the time,B and C are alternately)
1st hour: (A+B) = 10 units/hr
2nd hour: (A+C) = 9 units/hr
3rd hour: (A+B) = 10 units/hr
4th hour: (A+C) = 9 units/hr
5th hour: (A+B) = 10 units/hr
6th hour: (A+C) = 9 units/hr

When we add the above units, we get the total 57 units.

Apart from the 6 hours of operation, to get the total work 60 units, A has to work for half an hour
Because in one of hour work of A, we will get 6 units)

Hence, time taken to fill the tank = 6.5 hours.

3. Bucket A has twice the capacity as bucket B. It takes 54 turns for bucket A to fill the empty cistern. How many turns will it take for both the buckets A and B, having each turn together to fill the empty cistern?

 (A) 48 (B) 36 (C) 32 (D) 27

jQuery UI Accordion - Default functionality
It takes 54 turns for bucket A to fill the empty cistern.
Bucket A has twice the capacity as bucket B.
So, it will take 108 turns for bucket B to fill the empty cistern.

Total work = 108 units (L.C.M of 54, 108)

Work done by bucket A in 1 turn = 108/54 = 2 units
Work done by bucket B in 1 turn = 108/108 = 1 unit

If both the buckets are used simultaneously,
word done in 1 turn = 3 units (2+1 = 3)

No.of turns taken for both the buckets A and B, having each turn together to fill the empty cistern = 108/3 = 36 turns

4.  80 buckets of water fill a tank when the capacity of each bucket is 12. 5 liters. How many buckets will be needed to fill the same tank if the capacity of each bucket is 10 liters?

 (A) 100 (B) 110 (C) 120 (D) 130

jQuery UI Accordion - Default functionality
Total capacity of the tank = 80x12.5 = 1000 liters

If the capacity of the bucket is 10 liters, no. of buckets will be needed to fill the tank = 1000/10 = 100 buckets.

5. Taps A and B can fill a cistern in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 4 minutes, how much further time would it take for B to fill the cistern?

 (A) 5 min. (B) 6 min. (C) 7 min. (D) 8 min.

jQuery UI Accordion - Default functionality
Total work = 60 units (L.C.M of 12, 15)

Word done by tap A = 60/12 = 5 units/min.
Word done by tap B = 60/15 = 4 units/min.

Word done by A and B together = 9 units/min (5+4 = 9)

Both are opened together and A is closed after 4 minutes.
Word done by both A and B in 4 minutes = 9x4 = 36 units.

Remaining work to be done = 60 - 36 = 24 units.
This 24 units of work is completed by B alone.
In 1 min, B can do 4 units of work.
B can do 24 units in 24/4 = 6 min

Hence, further time taken by B to fill the tank is 6 min.

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