Pipes and Cisterns | Concepts and Examples

Pipes and Cisterns | Concepts and Examples

Pipes and Cisterns | Concepts and Examples

Introduction

Pipes and Cisterns problems are a common topic in quantitative aptitude exams. These problems are similar to Time and Work problems but involve pipes filling or emptying a tank (cistern). The key is to determine the time required to fill or empty the tank when multiple pipes are involved.

Basic Concepts

  1. Filling Pipes: These pipes fill the tank with water.
    • Example: A pipe can fill a tank in 5 hours, meaning it fills 1/5th of the tank per hour.
  2. Emptying Pipes: These pipes drain the tank.
    • Example: A pipe can empty a tank in 6 hours, meaning it empties 1/6th of the tank per hour.
  3. Net Inflow or Outflow:
    • If both filling and emptying pipes are open together, the net effect is calculated by subtracting the emptying pipe’s rate from the filling pipe’s rate.

Key Formulas

  1. Time taken by a pipe to fill the tank = Capacity of the tank / Rate of filling
  2. Time taken by a pipe to empty the tank = Capacity of the tank / Rate of emptying
  3. If a pipe fills a tank in ‘x’ hours, its rate of work = 1/x
  4. If a pipe empties a tank in ‘y’ hours, its rate of work = -1/y
  5. If two pipes (one filling, one emptying) are opened together, the time to fill/empty the tank is calculated as:Net Rate= Net Rate=(x/1​−y/1​)

Problem-Solving Methods

1. LCM Method (Quick Approach)

Instead of using fractions, take the LCM of the given numbers as the tank capacity and solve using unitary method.

Example:

A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. How long will it take to fill the tank if both are opened together?

Solution:

  • Assume LCM(6,8) = 24 as the tank capacity.
  • Filling rate = 24/6 = 4 units/hour
  • Emptying rate = 24/8 = 3 units/hour
  • Net inflow = 4 – 3 = 1 unit/hour
  • Time to fill = 24/1 = 24 hours

Types of Questions

1. Simple Pipe Filling

A pipe fills a tank in 5 hours. How much part of the tank will be filled in 2 hours?
Solution:

  • Rate of filling = 1/5 per hour
  • In 2 hours = (1/5) × 2 = 2/5 of the tank

2. Multiple Pipes Working Together

Two pipes fill a tank in 4 hours and 6 hours. Find the time taken if both work together.
Solution:

  • Rate of first pipe = 1/4 per hour
  • Rate of second pipe = 1/6 per hour
  • Total rate = (1/4 + 1/6) = 5/12 per hour
  • Time required = 12/5 = 2.4 hours (2 hours 24 minutes)

3. Pipes with Emptying Effect

A pipe fills a tank in 3 hours, but a leak drains it in 5 hours. How long will the tank take to fill?
Solution:

  • Rate of filling = 1/3 per hour
  • Rate of leak = 1/5 per hour
  • Net rate = (1/3 – 1/5) = 2/15 per hour
  • Time required = 15/2 = 7.5 hours

Shortcut Tricks

  1. LCM Method: Always assume LCM of given numbers as total capacity.
  2. Conversion to per-hour work: Express each pipe’s work as a fraction of 1 hour.
  3. Net effect: If both filling and emptying pipes are open, subtract the emptying rate from the filling rate.

Conclusion

Mastering Pipes and Cisterns requires strong basics in fractions, LCM, and work-time concepts. Practicing different types of questions will help in quick calculations and improve accuracy in competitive exams.

Pipes and Cisterns | Concepts and Examples