Pipe and cistern questions

Introduction to Pipe and cistern questions

Another format for time and work-based questions is the pipes and cistern. How long does it take to fill or empty a tank, how much work is required for the same and similar questions may be asked? Candidates should be aware of two things when confronted with this type of question:

An inlet is a pipe that connects to a tank and is used to fill it with water. In this case, it’s all positive.

An outlet is a pipe that connects to the tank’s water drain. Negative work can be seen in this example. The term ‘leak’ may also be used to describe it in the context of the question.

Tips and tricks to solve pipe and cistern questions

Candidates need to look for time-saving shortcuts in order to succeed in competitive exams, which are all about time management.

Here are a few pointers to speed up the process of solving word puzzles involving pipes and cisterns:

• There are a number of terms and formulas that one must be familiar with in order to understand the process of filling and emptying a tank. Only then will a candidate be able to answer these questions without getting tangled up in confusion.

• Make sure you don’t spend too much time on a single question if you can’t solve it.

• To better understand the concept, memorise the formulas and practise as much as possible.

Important points to solve pipe and cistern amplitude

• If a cistern can be filled in ‘x’ hours by an inlet pipe, then

Filling work done in 1 hour = 1/ x

• It is possible to empty a cistern in a time period of ‘y’ hours using an outlet pipe.

Empty work done in 1 hour = 1/y

• The net-work completed in one-hour = (filling work in one hour) – (Empty work in 1 hour)

W = 1/x – 1/y

• Total filling or emptying time of cistern

T = 1/W = x * y/ y- x

Some of the important questions of pipe and cistern amplitude

• In 30 minutes, 20 minutes, and 10 minutes, pipes A, B, and C can fill a tank from empty to full. Three pipes are opened when the tank is empty. When A, B, and C are activated, they release a variety of chemical solutions P, Q, and R. After three minutes, what is the solution R concentration in the liquid in the tank?

1. 6/11
2. 10/11
3. 4/5
4. 3/8

Answer: A

Explanation: Part filled by (A + B + C) in 3 minutes = 3(1/30+1/20+1/10) 

= 3 × 11/60 = 11/20

Part filled by C in 3 minutes =3/10

Required ratio = 3/10 × 20/11 

= 6/11

• By means of three pipes M, N, O, the tank is filled to the brim. The tank is completely filled in the same amount of time as if only the third pipe were to be used. In comparison to the first pipe, the second pipe fills the tank in 5 additional hours, and in comparison to the third pipe, in 4 additional hours. The first pipe takes the following amount of time:

1. 10 hours
2. 11hours
3. 15 hours
4. 16 hours

Answer: C

Explanation: If the first pipe alone takes y hours to fill the tank, then the tank will be full in y hours.

Filling the tank with the second and third pipes will take (y-5 )and ( y-9 )hours respectively.

1/y + 1/y-5 = 1/ y-9

= y-5+y / y(y-5) = 1/y-9

(2y – 5)(y – 9) = y(y – 5)

 y2 – 18y + 45 = 0

(y – 15)(y – 3) = 0

Hence y = 15 (3 can’t be taken)

• A tank can be filled in 15 minutes and a tank in 20 minutes by two pipes A and B. Both pipes are opened simultaneously, but pipe A is shut off after four minutes. In total, how long does it take to fill up the tank?

1. 23 min 40 sec
2. 14 min 40 sec
3. 14 min 50 sec
4. 16 min 50 sec

Answer: B

Explanation : Part filled in 4 minutes = 4(1/15+1/20) = 7/15

Remaining part = ( 1-7/15) = 8/15

Part filled by B in 1 minute = 1/20

So x = 8/15 × 1 × 20

= 10 min 40 sec

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

Conclusion

Questions about pipes and cisterns are very similar to those about time and work.

Problems with pipes and cisterns often involve calculating how much of the tank has been filled or emptied, which is similar to how much work has been completed over time.

Time spent filling or emptying a tank is the same as time spent working on a project.

There are a number of terms and formulas that one must be familiar with in order to understand the process of filling and emptying a tank. Only then will a candidate be able to answer these questions without getting tangled up in confusion.