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UGC NET Pipes & Cisterns

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This page covers UGC NET Pipes & Cisterns with complete concept notes, 5 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Pipes & Cisterns— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Key Rules

If a pipe fills a tank in 'n' hours, it fills 1/n part in 1 hour. This is the pipe's rate of work. When pipes work together, ADD their rates. For outlet pipes, SUBTRACT their rates from inlet rates.

The combined rate tells you the net filling or emptying speed

Core Formulas

- Pipe Rate = 1/Time taken to fill/empty alone - Combined Rate = Sum of individual rates (+ for inlet, - for outlet) - Time with combined rate = 1/Combined rate - Work done = Rate × Time

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC loves asking about 2-3 pipes working together, pipes opened at different times, and alternating pipe problems. Questions often mix inlet and outlet pipes to test your positive/negative rate concept.

ShortcutsUse these to save 30–60 seconds per question

Take LCM of all individual times. This becomes tank capacity. Each pipe's rate becomes LCM/individual time.

This eliminates fractions completely and makes calculations super fast.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Find individual rates A's rate = 1/12 per hour B's rate = 1/15 per hour C's rate = -1/20 per hour (negative for outlet)

2
Step 2

Combined rate = 1/12 + 1/15 - 1/20

3
Step 3

Take LCM of 12,15,20 = 60 A fills 60/12 = 5 units/hour B fills 60/15 = 4 units/hour C empties 60/20 = 3 units/hour

4
Step 4

Net rate = 5 + 4 - 3 = 6 units/hour

5
Step 5

Time = 60/6 = 10 hours Worked Example 2: Two pipes fill tank in 6 hours when opened together. First pipe alone takes 5 hours more than second pipe. Find individual times.

1
Step 1

Let second pipe take x hours, first takes (x+5) hours

2
Step 2

Combined rate = 1/6 per hour

3
Step 3

1/(x+5) + 1/x = 1/6

4
Step 4

Cross multiply: 6x + 6(x+5) = x(x+5)

5
Step 5

6x + 6x + 30 = x² + 5x

6
Step 6

12x + 30 = x² + 5x

7
Step 7

x² - 7x - 30 = 0

8
Step 8

(x-10)(x+3) = 0, so x = 10 hours

9
Step 9

Second pipe = 10 hours, First pipe = 15 hours Shortcut Trick 1 - Efficiency Method: Instead of fractions, use efficiency. If A completes work in 4 hours and B in 6 hours, their efficiencies are in ratio 6:4 = 3:2. Total work = LCM(4,6) = 12 units. Shortcut Trick 2 - Alternating Pipes Formula: If two pipes work alternately starting with first pipe, and their individual times are a and b hours, then cycles needed = Total work/(work in 2 hours) and check remainder. The #1 Most Common Trap: Students forget to make outlet pipe rates NEGATIVE. They add all rates as positive and get wrong answers. Always remember: Inlet = +, Outlet = -, then calculate combined rate. Another major mistake is not converting 'part of tank filled' back to actual time. If question asks when tank will be full and you calculated rate, don't forget the final division step.

Key Points to Remember

  • Inlet pipe rate = +1/time, Outlet pipe rate = -1/time to fill/empty alone
  • Combined rate = Sum of all individual rates (+ for inlet, - for outlet)
  • Time with multiple pipes = 1/Combined rate
  • LCM method eliminates fractions: Tank capacity = LCM of all individual times
  • Pipe efficiency = LCM/Individual time gives units filled per hour
  • When pipes opened at different times, calculate work done by each separately
  • If two pipes together take time T and alone take times in ratio a:b, individual times are T×(a+b)/b and T×(a+b)/a
  • Alternating pipes: Calculate work done in complete cycles first, then remainder
  • Three pipes A, B, C with rates 1/a, 1/b, 1/c together take time = abc/(bc+ac-ab) when C is outlet
  • Always verify: Combined rate positive means filling, negative means emptying

Exam-Specific Tips

  • If a pipe fills tank in n hours, it fills 1/n part of tank in 1 hour
  • Two pipes with individual times a and b hours together take ab/(a+b) hours when both are inlet pipes
  • If inlet pipe fills in a hours and outlet empties in b hours, together they take ab/(b-a) hours to fill
  • When three pipes A, B (inlet) and C (outlet) work together, time = abc/(bc+ac-ab) hours
  • Pipe opened for part time contributes: (Part time/Total individual time) × Tank capacity
  • Two pipes filling together in 6 hours with ratio 2:3 take individual times of 15 and 10 hours
  • If tank fills in x hours with inlet and empties in y hours with outlet, net time = xy/(y-x) hours
Practice MCQs

Pipes & Cisterns — Practice Questions

5graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A pipe can empty a full cistern in 8 hours. If the cistern is already 3/4 full, how long will it take for the pipe to empty it completely?

Practice 2easy

A pipe can empty a full cistern in 20 hours. If the cistern is already 3/4 full, how long will it take to empty it completely?

Practice 3medium

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Practice 4medium

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Practice 5hard

Two pipes A and B together can fill a tank in 10 hours. If Pipe A alone takes 6 hours more than Pipe B alone to fill the tank, how long will Pipe B take to fill the tank individually?

60-Second Revision — Pipes & Cisterns

  • Remember: Inlet rates are positive, outlet rates are negative always
  • Formula: Combined rate = Sum of individual rates, Time = 1/Combined rate
  • Trick: Use LCM method to avoid fractions in complex problems
  • Trap: Don't forget to subtract outlet pipe rates from total
  • Pattern: SSC asks 2-3 pipes together and alternating pipe problems most
  • Quick check: Combined rate positive = filling, negative = emptying
  • Time-saver: For two pipes a,b hours individually, together take ab/(a+b) hours
←Work & WagesEfficiency Problems→
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