Pipes & Cistern
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Solved Examples
Study MaterialSolved Examples – Pipes & Cisterns
Solved examples help students understand the practical application of filling rates, emptying rates, leakage concepts, combined work, and efficiency in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various aptitude examinations.
Topics Covered in Solved Examples
- Single Pipe Filling Problems
- Combined Pipe Problems
- Inlet and Outlet Questions
- Leakage Problems
- Efficiency Concepts
- Alternate Opening of Pipes
- Tank Emptying Problems
- Advanced Work-Rate Applications
Example 1: Single Pipe Filling Problem
Question: A pipe fills a tank in 5 hours. What fraction of the tank is filled in 1 hour?
Solution:
If a pipe fills a tank in 5 hours:
Work done in 1 hour:
= 1/5
Answer: 1/5 of the tank
Example 2: Combined Filling Problem
Question: Pipe A fills a tank in 6 hours and Pipe B fills it in 3 hours. In how many hours will both pipes together fill the tank?
Solution:
Pipe A’s work in 1 hour:
= 1/6
Pipe B’s work in 1 hour:
= 1/3
Combined work:
= 1/6 + 1/3
= 1/6 + 2/6
= 3/6
= 1/2
Time taken:
= 2 hours
Answer: 2 hours
Example 3: Inlet and Outlet Problem
Question: A pipe fills a tank in 8 hours and another pipe empties it in 12 hours. In how many hours will the tank be filled if both pipes are opened together?
Solution:
Filling work:
= 1/8
Emptying work:
= 1/12
Net work:
= 1/8 − 1/12
= 3/24 − 2/24
= 1/24
Time taken:
= 24 hours
Answer: 24 hours
Example 4: Leakage Problem
Question: A tank can be filled in 10 hours, but due to leakage it takes 15 hours. In how many hours can the leak empty the full tank?
Solution:
Without leak:
= 1/10
With leak:
= 1/15
Leakage work:
= 1/10 − 1/15
= 3/30 − 2/30
= 1/30
Leak alone empties tank in:
= 30 hours
Answer: 30 hours
Example 5: LCM Method Problem
Question: Pipe A fills a tank in 4 hours and Pipe B fills it in 6 hours. Find the time taken by both together using LCM method.
Solution:
LCM of 4 and 6 = 12
Pipe A fills:
= 12/4 = 3 units/hr
Pipe B fills:
= 12/6 = 2 units/hr
Combined work:
= 3 + 2
= 5 units/hr
Time taken:
= 12/5
= 2.4 hours
Answer: 2.4 hours
Example 6: Three Pipes Problem
Question: Three pipes can fill a tank in 12 hours, 15 hours, and 20 hours respectively. In how many hours will they together fill the tank?
Solution:
Combined work:
= 1/12 + 1/15 + 1/20
LCM = 60
= 5/60 + 4/60 + 3/60
= 12/60
= 1/5
Time taken:
= 5 hours
Answer: 5 hours
Example 7: Tank Emptying Problem
Question: A pipe empties a tank in 9 hours. What fraction of the tank is emptied in 1 hour?
Solution:
Work emptied in 1 hour:
= 1/9
Answer: 1/9 of the tank
Example 8: Alternate Opening Problem
Question: Pipe A fills a tank in 4 hours and Pipe B empties it in 6 hours. If both pipes are opened alternately for 1 hour each, in how many hours will the tank be filled?
Solution:
Pipe A fills in 1 hour:
= 1/4
Pipe B empties in 1 hour:
= 1/6
Net work in 2 hours:
= 1/4 − 1/6
= 3/12 − 2/12
= 1/12
Thus, 1/12 tank is filled every 2 hours.
Total time:
= 24 hours
Answer: 24 hours
Example 9: Efficiency Problem
Question: Pipe A is twice as efficient as Pipe B. If Pipe B fills a tank in 12 hours, in how many hours can Pipe A fill the tank?
Solution:
Efficiency is inversely proportional to time.
If A is twice as efficient:
Time taken by A:
= 12/2
= 6 hours
Answer: 6 hours
Example 10: Net Work Problem
Question: A pipe fills a tank in 20 hours while another empties it in 30 hours. Find the net work done in 1 hour.
Solution:
Net work:
= 1/20 − 1/30
= 3/60 − 2/60
= 1/60
Answer: 1/60 of the tank
Example 11: Partial Tank Problem
Question: A tank is half filled. Pipe A can fill the full tank in 8 hours. How much time will Pipe A take to fill the remaining half?
Solution:
Half tank remaining:
= 1/2
Pipe fills full tank in:
= 8 hours
Time for half tank:
= 8 × 1/2
= 4 hours
Answer: 4 hours
Example 12: Two Outlet Pipes Problem
Question: Two outlet pipes can empty a tank in 10 hours and 15 hours respectively. In how many hours will both together empty the tank?
Solution:
Combined emptying work:
= 1/10 + 1/15
= 3/30 + 2/30
= 5/30
= 1/6
Time taken:
= 6 hours
Answer: 6 hours
Example 13: Advanced Leakage Problem
Question: A cistern is normally filled in 8 hours, but due to leakage it takes 10 hours. Find the time taken by the leak to empty the full cistern.
Solution:
Without leak:
= 1/8
With leak:
= 1/10
Leak work:
= 1/8 − 1/10
= 5/40 − 4/40
= 1/40
Leak empties the tank in:
= 40 hours
Answer: 40 hours
Example 14: Combined Efficiency Problem
Question: Pipe A fills a tank in 9 hours and Pipe B fills it in 18 hours. Find the time taken when both work together.
Solution:
Combined work:
= 1/9 + 1/18
= 2/18 + 1/18
= 3/18
= 1/6
Time taken:
= 6 hours
Answer: 6 hours
Example 15: Complex Pipe Problem
Question: A pipe fills a tank in 5 hours and another empties it in 20 hours. If both pipes are opened together, what fraction of the tank is filled in 1 hour?
Solution:
Filling work:
= 1/5
Emptying work:
= 1/20
Net work:
= 1/5 − 1/20
= 4/20 − 1/20
= 3/20
Answer: 3/20 of the tank
Important Exam Tips
- Convert every problem into one-hour work.
- Use LCM method to avoid fractions.
- Remember outlet work is negative.
- Practice leakage questions regularly.
- Use direct efficiency methods.
- Improve fraction simplification speed.
- Practice previous year aptitude questions.
Common Mistakes to Avoid
- Ignoring outlet negative work.
- Using wrong combined formulas.
- Calculation mistakes in fractions.
- Ignoring leakage effects.
- Confusing efficiency and time relationships.
Practicing solved examples regularly improves conceptual clarity, calculation speed, and logical analysis in solving Pipes & Cisterns aptitude questions in competitive examinations.