Question

Three pipes $A, B$ and $C$ can fill a cistern in 10,12 and 15 hours, respectively, while working alone. If all the three pipes are opened together, the time taken to fill the cistem will be (a) 4 hours (b) 6 hours (c) 7 hours (d) None of these

Name: Problem 7, Chapter 14: The Pearson Guide to Objective Arithmetic for Competitive Examinations
Uploaded: 2021-12-21T05:03:23-08:00
Duration: 1 min 53 s
Channel: Hubert Agamasu
Description: Three pipes A, B and C can fill a cistern in 10,12 and 15 hours, respectively, while working alone. If all the three pipes are opened together, the time taken to fill the cistem will be (a) 4 hours (b) 6 hours (c) 7 hours (d) None of these

    Three pipes $A, B$ and $C$ can fill a cistern in 10,12 and 15 hours, respectively, while working alone. If all the three pipes are opened together, the time taken to fill the cistem will be
(a) 4 hours
(b) 6 hours
(c) 7 hours
(d) None of these

The Pearson Guide to Objective Arithmetic for Competitive Examinations

Dinesh Khattar 2nd Edition

Chapter 14, Problem 7

Instant Answer

Solved by Expert Hubert Agamasu

12/21/2021

Step 1

- Pipe A fills the cistern in 10 hours, so its rate is $ \frac{1}{10} $ of the cistern per hour. - Pipe B fills the cistern in 12 hours, so its rate is $ \frac{1}{12} $ of the cistern per hour. - Pipe C fills the cistern in 15 hours, so its rate is \( Show more…

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Three pipes $A, B$ and $C$ can fill a cistern in 10,12 and 15 hours, respectively, while working alone. If all the three pipes are opened together, the time taken to fill the cistem will be (a) 4 hours (b) 6 hours (c) 7 hours (d) None of these

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Key Concepts

Work Rate

Work rate is a measure of the amount of work completed per unit of time. It is fundamental in problems where multiple agents (such as machines, workers, or pipes) contribute to completing a task, often expressed as a fraction of the task completed in one unit of time.

Reciprocal Relationship between Time and Work

In work problems, the time taken to complete a task and the work rate are reciprocals of each other. This means that if the work rate of an agent is known, the time required to accomplish the entire work can be found by taking the reciprocal of that rate, making it a useful concept for transforming between time and rate.

Addition of Work Rates

When multiple agents work simultaneously, each with their own work rate, the overall rate of work is obtained by adding the individual rates together. This principle allows the calculation of the combined work time for a task by summing the rates and then taking the reciprocal of the total rate.

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