Pipes and cistern problems with solution - part 1

Introduction

Start learning the pipes and cisterns problems with solutions on Nithra Jobs, this sums will improve your skills that will be helpful for your career growth. In this article, we have provided pipes and cisterns formulas for better understanding. Begin to learn today and improve your hidden skills! If you are preparing for the government exams then you should prepare these sums because pipe and cistern questions for SSC are frequently asked, so start learning!!

Formulas:

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

2. If a pipe can fill a tank in x hours, then: part filled in 1 hour = 1/x.

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

4. 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, then the net part filled in 1 hour = 1/x - 1/y.

5. 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 on opening both the pipes, thenthe net part emptied in 1 hour = 1/y - 1/x.

Solved Problems

1. One pipe can fill a tank five times as fast as another pipe. If together the two pipes can fill the tank in 52 minutes, then the slower pipe alone will be able to fill the tank in:

Answer: 5.2 hrs.

Explanation:

Suppose the slower pipe alone can fill the tank in x minutes. Then the faster pipe can fill the tank in ( x / 5 ) minutes.

Part filled by the slower pipe in 1 minute = ( 1 / x )

Part filled by the faster pipe in 1 minute = 1 / ( x / 5 )

= 5 / x

Part filled by both the pipes in 1 minute = ( 1 / x ) + ( 5 / x )

Given that, both the pipes together can fill the tank in 52 minutes.

Part filled by both the pipes in 1 minute = ( 1 / 52 ) ( 1 / x ) + ( 5 / x )

= ( 1 / 52 ) ( 6 / x )

= 1 / 52 ( 6 × 52 ) = x

x = 312 minutes

x = ( 312 / 60 ) hrs

x = 5.2 hrs

The slower pipe alone will be able to fill the tank in 5.2 hrs.

2. One pipe can fill a tank twice as fast as another pipe. If together the two pipes can fill the tank in 14 minutes, then the slower pipe alone will be able to fill the tank in?

Answer: 21 min

Explanation:

Let one pipe taken x hours to fill the tank

Then, ( 1 / x ) + ( 1 / 2x ) = ( 1 / 14 )

( 2 + 1 ) / 2x = ( 1 / 14 )

3 / 2x = 1 / 14

x = ( 3 / 2 ) × 14

= 21 min

The slower pipe alone will be able to fill the tank in 21 minutes.

3. Two pipes will fill the cistern in 15 hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened. In how much time the cistern will be filled?

Answer: 10 hours.

Explanation:

Two pipes can fill the cistern in 1 hr.

= ( 1 / 15 ) + ( 1 / 12 )

Pipe empty the cistern in 1 hr.

= 1 / 20

Work done by all the tanks working together in 1 hr.

= [ ( 1 / 15 ) + ( 1 / 12 ) ] - ( 1 / 20 )

= ( 4 + 5 - 3 ) / 60

= ( 9 - 3 ) / 60

= ( 6 / 60 )

= ( 1 / 10 )

= 10 hours.

The cister will be filled in 10 hours.

4. Two pipes can fill a tank in 8 hours and 10 hours. While a third pipe empties the full tank in 12 hours. If all three pipes are operated simultaneously, In how much time will the tank be filled?

Answer: 120 / 17 hours

Explanation:

Given, time taken by two tap to fill the tank = 8 hours, 10 hours

Time taken by third tap to empty the tank = 12 hours

Time taken by all tap together to fill the tank = ( 1 / 8 ) + ( 1 / 10 ) - ( 1 / 12 )

= ( 15 + 12 - 10 ) / 120

= 17 / 120

Time taken by all tap together to fill the tank = 120 / 17 hours.

5. Two pipes can fill a tank in 12 hours and 15 hours. If two pipes are operate simultaneously, In how much time will the tank be filled?

Answer: 20 / 3 hours

Explanation:

Given, time taken by two tap to fill the tank = 12 hours, 15 hours

Time taken by all tap together to fill the tank = ( 1 / 12 ) + ( 1 / 15 )

= ( 12 + 15 ) / 180

= 27 / 180

= 3 / 20

Time taken by all tap together to fill the tank = 20 / 3 hours.

Conclusion

Pipes and cisterns tricks are given above, and we are also providing unsolved pipes and cisterns questions on our website, which will make you practice and get rid of the exam fears. On Nithra Jobs, thousands of jobs for freshers, and experienced candidates are waiting, if you are searching for a job in Tamil Nadu, visit our site and grab your jobs!!