Theory & Concepts
SSC CGL Pipes and Cisterns Questions, Formulas & Tricks
Prepare Pipes and Cisterns for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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Practice Notes
18 min readDifficulty: Intermediate
Pipes and cisterns is a direct application of the time and work logic. The only difference is the concept of "negative work"—where an outlet pipe or a leak empties the tank while inlet pipes fill it.
In the Ssc cgl exam, questions often combine multiple inlet pipes with a leak at the bottom. Mastering the "Net Efficiency" method using LCM is the most efficient way to reach the answer without getting bogged down in messy fractions.
Learning path
- Inlet vs Outlet efficiency
- Calculating net filling time
- Cistern capacity problems
- 10 standard solved problems
- Alternate day/pipe logic
1. Basic concepts
The pipe rule
If a pipe can fill a tank in hours, then the part filled in hour is:
If a pipe can empty a full tank in hours, then the part emptied in hour is:
2. Net filling time
When pipes (inlet) and (outlet) are opened together:
3. Solved examples
Question 01Standard pattern
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is:
12 minutes
15 minutes
25 minutes
10 minutes
Correct answer: a) 12 minutes
Solution
Total Capacity (LCM of 20, 30) = \( 60 \text{ units} \).
Efficiency of A = \( 60/20 = 3 \text{ units/min} \).
Efficiency of B = \( 60/30 = 2 \text{ units/min} \).
Combined efficiency = \( 3 + 2 = 5 \text{ units/min} \).
Time taken = \( 60 / 5 = 12 \text{ minutes} \).
Question 02Standard pattern
A pipe can fill a tank in 16 hours. Due to a leak in the bottom, it is filled in 24 hours. If the tank is full, how much time will the leak take to empty it?
48 hours
32 hours
40 hours
36 hours
Correct answer: a) 48 hours
Solution
Total Capacity (LCM of 16, 24) = \( 48 \text{ units} \).
Efficiency of filling pipe = \( 48/16 = 3 \text{ units/hr} \).
Efficiency of (Pipe + Leak) = \( 48/24 = 2 \text{ units/hr} \).
Efficiency of leak = \( 2 - 3 = -1 \text{ unit/hr} \).
Time for leak to empty full tank = \( 48 / 1 = 48 \text{ hours} \).
Question 03Standard pattern
Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe emties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?
7.5 hours
8 hours
10 hours
9 hours
Correct answer: a) 7.5 hours
Solution
LCM of 10, 12, 20 = \( 60 \text{ units} \).
Efficiencies: \( A = 6, B = 5, C = -3 \).
Net efficiency = \( 6 + 5 - 3 = 8 \text{ units/hr} \).
Time = \( 60 / 8 = 7.5 \text{ hours} \).
Question 04Standard pattern
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all are open, in how many hours will the tank be full?
3 hours
3.5 hours
2.5 hours
4 hours
Correct answer: a) 3 hours
Solution
LCM of 5, 10, 30 = \( 30 \text{ units} \).
Efficiencies: \( A = 6, B = 3, C = 1 \).
Total efficiency = \( 6 + 3 + 1 = 10 \text{ units/hr} \).
Time = \( 30 / 10 = 3 \text{ hours} \).
Question 05Standard pattern
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
14 hours
12 hours
16 hours
10 hours
Correct answer: a) 14 hours
Solution
Part filled in 2 hours = \( 2/6 = 1/3 \).
Remaining part = \( 1 - 1/3 = 2/3 \).
A+B fill \( 2/3 \) in \( 7 \text{ hours} \implies \) Full tank in \( 21/2 = 10.5 \text{ hours} \).
Efficiency of (A+B) = \( 60/10.5 \)? Let's use 1 hour work.
Work of C in 1 hr = \( 1/6 - 1/10.5 = 1/6 - 2/21 = \frac{7-4}{42} = 3/42 = 1/14 \).
Time for C = \( 14 \text{ hours} \).
Question 06Standard pattern
A tank has a leak which would empty it in 8 hours. A tap is turned on which admits 6 litres a minute into the tank, and it is now emptied in 12 hours. How many litres does the tank hold?
8640 litres
8000 litres
9000 litres
7200 litres
Correct answer: a) 8640 litres
Solution
Leak alone = \( 8 \text{ hrs} \). (Leak + Tap) = \( 12 \text{ hrs} \).
Total capacity units (LCM 8, 12) = \( 24 \). Eff: \( L = -3, (L+T) = -2 \).
Tap Efficiency = \( -2 - (-3) = 1 \text{ unit/hr} \).
Time for Tap alone to fill = \( 24 / 1 = 24 \text{ hours} \).
Water added by tap in 24 hrs = \( 24 \times 60 \times 6 \text{ litres} \).
Calculation: \( 1440 \times 6 = 8640 \text{ litres} \).
Question 07Standard pattern
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
30 minutes
15 minutes
25 minutes
20 minutes
Correct answer: a) 30 minutes
Solution
LCM = \( 120 \). Eff: \( A=2, B=3 \).
Let total time be \( 2x \) minutes.
Units added in first half (B only): \( 3 \times x = 3x \).
Units added in second half (A+B): \( (2+3) \times x = 5x \).
Total: \( 3x + 5x = 120 \implies 8x = 120 \implies x = 15 \).
Total Time \( 2x = 30 \text{ minutes} \).
Question 08Standard pattern
A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?
10 minutes
8 minutes
12 minutes
15 minutes
Correct answer: a) 10 minutes
Solution
LCM (12, 15, 20) = \( 60 \). Eff: \( A=5, B=4, (A+B+C)=3 \).
Efficiency of waste pipe C = \( 3 - (5+4) = -6 \text{ units/min} \).
Time for C to empty = \( 60 / 6 = 10 \text{ minutes} \).
Question 09Standard pattern
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
144 minutes
108 minutes
120 minutes
130 minutes
Correct answer: a) 144 minutes
Solution
Efficiency Ratio: \( Fast : Slow = 3 : 1 \).
Total Efficiency = \( 3 + 1 = 4 \).
Total Capacity = \( 36 \times 4 = 144 \text{ units} \).
Time for slower pipe (eff 1) = \( 144 / 1 = 144 \text{ minutes} \).
Question 010Standard pattern
Capacity of a tank is 600 litres. Two pipes can fill it in 10 and 15 hours. If both are opened, how much water will be in the tank after 2 hours?
200 litres
250 litres
150 litres
300 litres
Correct answer: a) 200 litres
Solution
Efficiencies: \( 600/10 = 60, 600/15 = 40 \text{ litres/hr} \).
Combined filling rate = \( 60 + 40 = 100 \text{ litres/hr} \).
Water after 2 hours = \( 100 \times 2 = 200 \text{ litres} \).
4. Strategy errors to avoid
Error 01Sign oversight: Forgetting to treat outlet pipes as negative efficiency (-ve) in the net calculation.
Error 02LCM distraction: Not finding a common denominator (Total Capacity) for pipes with wildly different filling/emptying times.
Error 03Unit mismatch: Not converting 'litres per minute' to match 'hours' when solving for total capacity.
Error 04Closing too early: Not accounting for the work done while both pipes were working before one was closed.
