Processing math: 100%

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Pipes and Cistern

In pipes and cistern suppose, a water tank or a cistern is connected with two types of pipes to fill and empty it.

(i) Inlet: The pipe which fills the tank up is called an inlet.

(ii) Outlet: The pipe which empties the tank is called an outlet.

If an inlet fills up the cistern in 5 hours, then in 1 hour it fills up 1/5₀ part of it. We say that the work done by inlet in 1 hour is ¹/₅.

Rule 1. Suppose a pipe fills a tank in n hours.

Then, part of the tank filled in 1 hour = 1n, i.e., work done by the inlet in 1 hour= 1n


Rule 2. Suppose an outlet empties a full tank in m hours.

Then, part of the tank emptied in 1 hour = 1m, i.e., work done by the outlet in 1. hour = 1m

Solved Problems on Pipes and Cistern 1. A tap A can fill a cistern in 8 hours while tap B can fill it in 4 hours. In how much times will the cistern be filled if both A and B are opened together?

Solution:

Time taken by tap A to fill the cistern = 8 hours.

Work done by tap A in 1 hour = ¹/₈

Time taken by tap B to fill the cistern = 4 hours.

Work done by tap B in 1 hour = ¹/₄

Work done by (A + B) in 1 hour = (¹/₈ + ¹/₄) = ³/₈

Therefore, time taken by (A + B) to fill the cistern = ⁸/₃ hours = 2 hours 40 min.

2. A tap A can fill a cistern in 4 hours and the tap B can empty the full cistern in 6 hours. If both the taps are opened together in the empty cistern, in how much time will the cistern be filled up?

Solution:

Time taken by tap A to fill the cistern = 4 hours.

Work done by tap A in 1 hour = 1/4ᵗʰ

Time taken by tap B to empty the full cistern = 6 hours.

Work done by tap B in 1 hour = -1/6ᵗʰ (since, tap B empties the cistern).

Work done by (A + B) in 1 hour (¹/₄ - ¹/₆) = (3 - 2)/12 = 1/12th  part of the tank is filled.

Therefore, the tank will fill the cistern = 12 hours.

3. A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

Solution:

Time taken by tap A to fill the cistern = 12 hours.

Time taken by tap B to fill the cistern = 16 hours.

Time taken by tap C to empty the full cistern = 8 hours.

A’s 1 hour’s work = ¹/₁₂

B’s 1 hour’s work = ¹/₁₆

C’s 1 hour’s work = 18  (cistern being emptied by C)


Therefore, (A + B + C)’s 1 hours net work= (¹/₁₂ + ¹/₁₆ - ¹/₈) = ¹/₄₈

Therefore, time taken by (A + B + C) to fill the cistern = 48 hours.

4. A tank can be filled by two taps A and B in 8 hours and 10 hours respectively. The full tank can be emptied by a third tap C in 9 hours. If all the taps are turned on at the same time, in how much time will the empty tank be filled up completely?

Solution:

Time taken by tap A to fill the tank = 8 hours.

Time taken by tap B to fill the tank = 10 hours.

Time taken by tap C to empty the full tank = 9 hours.

A’s 1 hour’s work = ¹/₈

B’s 1 hour’s work = ¹/₁₀

C’s 1 hour’s work = 19  (cistern being emptied by C)


Therefore, (A + B + C)’s 1 hours net work= (¹/₈ + ¹/₁₀ - ¹/₉) = (45 + 36 – 40)/360 = ⁴¹/₃₆₀

Thus, tank will be filled completely in 36041 hours, when all the three are opened together. 


5. A cistern can be filled by one tap in 5 hours and by another in 4 hours. How long will it take to fill if both the taps are opened simultaneously?

Solution:

Time taken by first tap to fill the cistern = 5 hours.

Work done by first tap in 1 hour = ¹/₅

Time taken by second tap to fill the cistern = 4 hours.

Work done by second tap in 1 hour = ¹/₄

Work done by (first tap + second tap) in 1 hour = (¹/₅ + ¹/₄) = ⁹/₂₀

Therefore, time taken by (first tap + second tap) to fill the cistern = 209 hours. 


 Time and Work

Time and Work

Pipes and Cistern

Practice Test on Time and Work


 Time and Work - Worksheets

Worksheet on Time and Work









8th Grade Math Practice

From Pipes and Cistern to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More