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Pipes & Cisterns

Quantitative Aptitude / DI · Arithmetic Applications

Useful for: SSC CGL, Railway RRB, IBPS Banking, OSSC RHT — Regular High School Teacher, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Science, OSSC Mathematics, OSSSC Govt Physical Education Teacher (PET)

and 5 more exams

OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM, SSB Lecturer (Degree Colleges), SSB TGT PCM

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Overview

Man-days and efficiency link workers, days and hours; pipes are workers with positive or negative rates.

Key points

Work equivalence: M1D1H1/W1 = M2D2H2/W2.
More workers → fewer days (inverse); more work → more days (direct).
Leak: if a pipe fills in t1 hours but takes t2 with a leak, the leak alone empties in t1·t2/(t2 − t1).
Alternate-day work: find work done in one 2-day cycle.
Efficiency % comparison: if A is 25% more efficient, time ratio A:B = 4:5.

Explanation

Convert men, women and children to a common unit of efficiency.
For pipes opened at different times, compute the work done in each interval.
A cistern problem is unchanged if "fill" is replaced by "do the work".
Check that a net negative rate means the tank empties.

Step by step

Write the equivalence equation.
Substitute values.
Check direct or inverse variation.

Examples

12 men finish a job in 10 days; 8 men will take 12 × 10/8 = 15 days.
A pipe fills a tank in 6 h; with a leak it takes 8 h → leak empties a full tank in 6 × 8/(8 − 6) = 24 h.
A fills in 20 min, B in 30 min, C empties in 15 min; all open: 1/20 + 1/30 − 1/15 = 1/60 → 60 min.

Traps and advanced points

Trap: Multiplying instead of dividing when workers increase.
Trap: Adding an emptying pipe’s rate.
Trap: Ignoring hours per day when it changes.

Quick revision

M·D·H/W constant.
Leak time = t1t2/(t2 − t1).
Common efficiency unit for mixed workers.

Practice MCQs

A pipe fills a tank in 15 min and an outlet empties it in 35 min. If both are open, how long to fill the empty tank?
1. 23.62
2. 26.25
3. 28.87
4. 31.5
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Answer: (b) 26.25. Net rate = fill rate − empty rate.
A pipe fills a tank in 26 min and an outlet empties it in 54 min. If both are open, how long to fill the empty tank?
1. 55.16
2. 50.14
3. 60.17
4. 45.13
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Answer: (b) 50.14. Net rate = fill rate − empty rate.
A pipe fills a tank in 37 min and an outlet empties it in 80 min. If both are open, how long to fill the empty tank?
1. 75.72
2. 68.84
3. 82.6
4. 61.95
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Answer: (b) 68.84. Net rate = fill rate − empty rate.
A pipe fills a tank in 48 min and an outlet empties it in 99 min. If both are open, how long to fill the empty tank?
1. 102.49
2. 93.18
3. 83.86
4. 111.81
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Answer: (b) 93.18. Net rate = fill rate − empty rate.
A pipe fills a tank in 59 min and an outlet empties it in 118 min. If both are open, how long to fill the empty tank?
1. 141.6
2. 129.8
3. 106.2
4. 118
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Answer: (d) 118. Net rate = fill rate − empty rate.
A pipe fills a tank in 34 min and an outlet empties it in 71 min. If both are open, how long to fill the empty tank?
1. 78.29
2. 58.72
3. 65.24
4. 71.77
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Answer: (c) 65.24. Net rate = fill rate − empty rate.
A pipe fills a tank in 71 min and an outlet empties it in 147 min. If both are open, how long to fill the empty tank?
1. 151.06
2. 137.33
3. 164.79
4. 123.6
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Answer: (b) 137.33. Net rate = fill rate − empty rate.
A pipe fills a tank in 63 min and an outlet empties it in 130 min. If both are open, how long to fill the empty tank?
1. 122.24
2. 146.69
3. 134.46
4. 110.01
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Answer: (a) 122.24. Net rate = fill rate − empty rate.
A pipe fills a tank in 96 min and an outlet empties it in 194 min. If both are open, how long to fill the empty tank?
1. 228.05
2. 190.04
3. 209.04
4. 171.04
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Answer: (b) 190.04. Net rate = fill rate − empty rate.
A pipe fills a tank in 12 min and an outlet empties it in 26 min. If both are open, how long to fill the empty tank?
1. 20.06
2. 22.29
3. 24.51
4. 26.74
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Answer: (b) 22.29. Net rate = fill rate − empty rate.
A pipe fills a tank in 101 min and an outlet empties it in 202 min. If both are open, how long to fill the empty tank?
1. 181.8
2. 242.4
3. 222.2
4. 202
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Answer: (d) 202. Net rate = fill rate − empty rate.
A pipe fills a tank in 35 min and an outlet empties it in 74 min. If both are open, how long to fill the empty tank?
1. 66.41
2. 73.05
3. 79.69
4. 59.77
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Answer: (a) 66.41. Net rate = fill rate − empty rate.
A pipe fills a tank in 11 min and an outlet empties it in 23 min. If both are open, how long to fill the empty tank?
1. 21.08
2. 18.97
3. 23.19
4. 25.3
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Answer: (a) 21.08. Net rate = fill rate − empty rate.
A pipe fills a tank in 25 min and an outlet empties it in 51 min. If both are open, how long to fill the empty tank?
1. 53.94
2. 49.04
3. 58.85
4. 44.13
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Answer: (b) 49.04. Net rate = fill rate − empty rate.
A pipe fills a tank in 66 min and an outlet empties it in 132 min. If both are open, how long to fill the empty tank?
1. 118.8
2. 132
3. 158.4
4. 145.2
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Answer: (b) 132. Net rate = fill rate − empty rate.