Q5. A reservoir has two pipes, A and B. Pipe A can fill the reservoir in 12 hours. Pipe B takes 15 hours to
fill the reservoir. There is another waste pipe which can empty the reservoir. When all the pipes are
opened, the reservoir is full in 20 hours. How long will the waste pipe take to empty the full reservoir?
1. 12 hours
2. 9 hours
3. 10 hours
4. 15 hours

How to Solve Pipe and Reservoir Problems – Step-by-Step Approach

Pipe and reservoir problems are common in competitive exams like CSIR NET Life Science, IIT JAM, GATE Biotechnology, and DBT JRF. These problems test your understanding of rates of work, filling and emptying times, and how to handle combined rates of multiple sources. Let’s explore a typical pipe and reservoir problem and learn the method to solve it efficiently.

---

Pipe and Reservoir Problem Overview

Problem Statement:

A reservoir has two pipes, A and B.

• Pipe A can fill the reservoir in 12 hours.
• Pipe B can fill the reservoir in 15 hours.
• A waste pipe is connected to the reservoir, which empties it at a certain rate.
• When all three pipes are opened together, the reservoir gets full in 20 hours.

Objective:

Find how long the waste pipe will take to empty the reservoir.

---

Step-by-Step Solution

Step 1: Work Rate of Individual Pipes

Work rate of Pipe A:

1/12 of the reservoir per hour

Work rate of Pipe B:

1/15 of the reservoir per hour

Step 2: Combined Work Rate with Waste Pipe Open

Let the waste pipe’s emptying rate be x (fraction of reservoir emptied per hour).
According to the problem:

 

 

Step 3: Solve the Equation

Find the LCM of 12, 15, and 20, which is 60.
Convert the equation into a simplified form:

Rearranging terms:

 

Therefore, the waste pipe will take 10 hours to empty the full reservoir.

---

Correct Answer:

✅ Option 3: 10 hours

---

Concept of Pipe and Reservoir Problems

1. Filling Rate:

The rate at which a pipe fills the reservoir is the reciprocal of the time it takes to fill it.
For example, if a pipe fills the reservoir in 12 hours, its filling rate is 1/12 per hour.

2. Emptying Rate:

The rate at which a waste pipe empties the reservoir is the reciprocal of the time it takes to empty it.
If a waste pipe empties the reservoir in x hours, its emptying rate is 1/x per hour.

3. Combined Rate:

When multiple pipes are involved, the net filling rate is calculated as:

                         Net Rate=(Filling rates)−(Emptying rates)

If the reservoir fills completely in T hours, the combined rate is 1/T.

---

Tips to Solve Pipe and Reservoir Problems

1. Express the filling and emptying rates as fractions of work per hour.
2.  Find the combined rate when all pipes are open.
3.  Solve the equation step-by-step using LCM for simplification.
4.  Check the final answer by substituting back into the equation.

---

Importance of Pipe and Reservoir Problems in Competitive Exams

Pipe and reservoir problems are frequently tested in quantitative sections of competitive exams like:

• CSIR NET Life Science
• IIT JAM
• GATE Biotechnology
• DBT JRF

Solving these problems helps improve your logical reasoning and calculation speed.

---

Why Choose Let’s Talk Academy for CSIR NET Life Science Preparation?

1 Expert faculty with years of experience in CSIR NET and competitive exam preparation.
2 Comprehensive study materials and online test series.
3 Focused training on quantitative aptitude, reasoning, and life science topics.
4 Proven track record of success in CSIR NET, IIT JAM, and GATE Biotechnology.

➡️ Join Let’s Talk Academy for expert guidance and structured learning.

---

Conclusion

Pipe and reservoir problems are a common type of quantitative aptitude question in competitive exams. By understanding the filling and emptying rates and setting up equations correctly, you can solve these problems easily. For expert coaching and structured preparation, enroll at Let’s Talk Academy – the best institute for CSIR NET Life Science, IIT JAM, GATE Biotechnology, and DBT JRF.