Railway Group D Pipes and Cisterns Notes – Key Concepts & Practice Problems

Railway Group D Pipes and Cisterns Notes – Key Concepts & Practice Problems

Mastering Pipes and Cisterns problems is crucial for the Railway Group D examination, as these questions assess your understanding of work and time concepts applied to fluid dynamics. A solid grasp of these topics will enhance your problem-solving skills and boost your performance in the quantitative aptitude section.

Key Concepts and Formulas

1. Inlet and Outlet Pipes:

   • Inlet: A pipe that fills a tank.
   • Outlet: A pipe that empties a tank.

2. Filling and Emptying Rates:

   • If an inlet pipe fills a tank in 'A' hours, then the part filled in 1 hour is $\frac{1}{A}$.
   • If an outlet pipe empties a tank in 'B' hours, then the part emptied in 1 hour is $\frac{1}{B}$.

3. Combined Work:

   • If both inlet and outlet pipes are opened simultaneously, the net part of the tank filled in 1 hour is $\frac{1}{A} - \frac{1}{B}$.

4. General Formula:

   • Time taken to fill the tank when both pipes are open: $\frac{AB}{B - A}$ hours, provided $B > A$.

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Sample Problems

Problem 1: An inlet pipe can fill a tank in 6 hours, while an outlet pipe can empty the same tank in 9 hours. If both pipes are opened together, how long will it take to fill the tank?

Solution:

• Part filled by inlet in 1 hour: $\frac{1}{6}$
• Part emptied by outlet in 1 hour: $\frac{1}{9}$
• Net part filled in 1 hour: $\frac{1}{6} - \frac{1}{9} = \frac{3 - 2}{18} = \frac{1}{18}$
• Time taken to fill the tank: 18 hours.

Problem 2: Two inlet pipes can fill a tank in 12 hours and 15 hours, respectively. An outlet pipe can empty the tank in 20 hours. If all three pipes are opened together, how long will it take to fill the tank?

Solution:

• Part filled by first inlet in 1 hour: $\frac{1}{12}$
• Part filled by second inlet in 1 hour: $\frac{1}{15}$
• Part emptied by outlet in 1 hour: $\frac{1}{20}$
• Net part filled in 1 hour: $\frac{1}{12} + \frac{1}{15} - \frac{1}{20} = \frac{5 + 4 - 3}{60} = \frac{6}{60} = \frac{1}{10}$
• Time taken to fill the tank: 10 hours.

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Practice Questions

1. An inlet pipe fills a tank in 8 hours, and an outlet pipe empties it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
2. Two inlet pipes can fill a tank in 10 hours and 20 hours, respectively. An outlet pipe can empty the tank in 30 hours. If all three pipes are opened together, how long will it take to fill the tank?
3. An inlet pipe can fill a tank in 5 hours, but due to a leak at the bottom, it takes 7 hours to fill the tank. How long will it take for the leak to empty the full tank?

Answers:

1. 24 hours
2. 7.5 hours
3. 17.5 hours

Categories:

• Railway Group D Study Material
• Quantitative Aptitude Preparation
• Pipes and Cisterns Problems