Pipe & Cisterns
Quick Recap
- If a pipe fills a tank in x minutes, its one-minute work is 1/x.
- If two pipes work together, add their rates: 1/a + 1/b.
- If an outlet empties a tank, subtract its rate from the filling rate.
- Total work = rate × time.
- Time = total work / combined rate.
- If pipes are opened or closed at different times, calculate work interval by interval.
- For mixture pipes, proportion of a solution = quantity of that solution / total quantity filled.
Q1. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both pipes are opened together, but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
Correct Option: D
Rationale:
A’s rate = 1/15
B’s rate = 1/20
Together in 4 minutes:
4 × (1/15 + 1/20)
= 4 × 7/60
= 7/15
Remaining work = 8/15
After A is closed, B alone fills the remaining part:
Time = 8/15 × 20 = 32/3 minutes = 10 min 40 sec
Total time = 4 min + 10 min 40 sec = 14 min 40 sec.
Q2. Four pipes can fill a reservoir in 15, 20, 30 and 60 hours respectively. The first pipe is opened at 8 am, the second at 9 am, the third at 10 am and the fourth at 11 am. When will the reservoir be full?
Correct Option: D
Rationale:
From 8 to 9:
Work = 1/15
From 9 to 10:
Work = 1/15 + 1/20 = 7/60
From 10 to 11:
Work = 1/15 + 1/20 + 1/30 = 3/20
Total work done till 11 am:
1/15 + 7/60 + 3/20
= 4/60 + 7/60 + 9/60
= 20/60 = 1/3
Remaining work = 2/3
All four pipes together:
1/15 + 1/20 + 1/30 + 1/60 = 1/6
Time required = 2/3 ÷ 1/6 = 4 hours
Reservoir will be full at 3:00 pm.
Q3. Two pipes A and B can fill a tank in 20 minutes and 25 minutes respectively. Both are opened together, but after some time B is closed. The tank is filled in 14 minutes 40 seconds. For how long was B open?
Correct Option: F
Rationale:
Total time = 14 min 40 sec = 44/3 minutes
A works for the full time:
A’s work = 44/3 × 1/20 = 11/15
Remaining work = 4/15
This remaining work is done by B:
x/25 = 4/15
x = 20/3 minutes = 6 min 40 sec
So B was open for 6 min 40 sec, which is not in the given options.
Q4. Three pipes X, Y and Z can fill a tank in 24, 12 and 8 minutes respectively. All three pipes are opened together when the tank is empty. Pipe X fills Solution A, Pipe Y fills Solution B and Pipe Z fills Solution C. After 4 minutes, what is the proportion of Solution C in the tank?
Correct Option: A
Rationale:
In 4 minutes, Solution C filled by pipe Z:
4 × 1/8 = 1/2
Total filled by all pipes in 4 minutes:
4 × (1/24 + 1/12 + 1/8)
= 4 × 1/4
= 1
Therefore, proportion of Solution C = 1/2.
Q5. Two pipes A and B together can fill a cistern in 4 hours. B takes 6 hours more than A when working alone. How much time will A take alone?
Correct Option: B
Rationale:
Let A take x hours.
Then B takes x + 6 hours.
Together:
1/x + 1/(x + 6) = 1/4
(2x + 6) / (x² + 6x) = 1/4
x² + 6x = 8x + 24
x² – 2x – 24 = 0
x = 6
So A alone takes 6 hours.
Q6. Two outlet pipes P and Q are connected to a full tank. Pipe P alone can empty the tank in 12 minutes and pipe Q alone can empty it in 18 minutes. If both pipes are opened together, how long will it take to empty the tank completely?
Correct Option: D
Rationale:
P’s emptying rate = 1/12
Q’s emptying rate = 1/18
Together:
1/12 + 1/18 = 5/36
Time required = 1 ÷ 5/36 = 36/5 = 7.2 minutes.
Q7. Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 minutes?
Correct Option: A
Rationale:
A works for the full 18 minutes.
A’s work = 18/24 = 3/4
Remaining work = 1/4
This remaining work must be done by B:
x/32 = 1/4
x = 8 minutes
So B should be closed after 8 minutes.
Q8. A cistern is normally filled in 6 hours but takes 4 hours longer to fill because of a leak in its bottom. If the cistern is full, in how much time will the leak empty it?
Correct Option: A
Rationale:
Normal filling rate = 1/6
Due to leak, tank fills in 10 hours.
Net filling rate = 1/10
Leak rate:
1/6 – 1/10 = 4/60 = 1/15
So the leak will empty the full cistern in 15 hours.
Q9. Two pipes P and Q can fill a cistern in 12 minutes and 15 minutes respectively. Both pipes are opened together, but at the end of 3 minutes pipe P is closed. How much longer will the cistern take to fill completely?
Correct Option: A
Rationale:
P’s rate = 1/12
Q’s rate = 1/15
Work done in first 3 minutes:
3 × (1/12 + 1/15)
= 3 × 9/60
= 27/60 = 9/20
Remaining work = 11/20
After P is closed, Q alone works:
Time = 11/20 × 15 = 33/4 = 8 1/4 minutes.
Q10. A water tank has three taps A, B and C. A fills 4 buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together, a full tank is filled in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?
Correct Option: E
Rationale:
A fills 4 buckets in 24 minutes.
A’s rate = 1/6 bucket per minute
B fills 8 buckets in 60 minutes.
B’s rate = 2/15 bucket per minute
C fills 2 buckets in 20 minutes.
C’s rate = 1/10 bucket per minute
Combined rate:
1/6 + 2/15 + 1/10
= 5/30 + 4/30 + 3/30
= 12/30 = 2/5 bucket per minute
In 2 hours = 120 minutes:
Total buckets = 120 × 2/5 = 48 buckets
Capacity = 48 × 5 = 240 litres.
Q11. Three taps have diameters of 1 cm, 0.5 cm and 2 cm respectively. The rate of water flow through each tap is proportional to the square of its diameter. The tap with the largest diameter can fill the tank by itself in 61 minutes. If all three taps are opened together, how long will it take to fill the tank completely?
Correct Option: F
Rationale:
Diameters are 1 cm, 0.5 cm and 2 cm.
Flow rates are proportional to square of diameter:
1² : 0.5² : 2²
= 1 : 0.25 : 4
The largest tap has rate 4 units and fills the tank in 61 minutes.
Total work = 4 × 61 = 244 unit-minutes
All taps together rate:
1 + 0.25 + 4 = 5.25 units
Time = 244 / 5.25 = 46.48 minutes approximately.
This value is not in the given options.
Pipe and Cisterns Questions for CET 2026 Quant Preparation
Pipe and Cisterns is an important arithmetic topic for CET 2026, MBA entrance exams, banking exams, aptitude tests and placement preparation. These questions are based on work rate, tank filling, tank emptying, inlet pipes, outlet pipes, leaks, taps, reservoirs and combined efficiency. A strong command of pipe and cistern problems helps students solve time and work questions faster because both topics use the same concept of unit work. In competitive exams, pipe and cistern questions often include pipes opening and closing at different times, multiple taps working together, leakage cases, proportional flow rates and mixture-based tank filling. Regular practice improves calculation speed, fraction handling and logical understanding of rates. This quiz is designed with detailed solutions so students can check answers instantly and understand the correct method step by step. Use this Pipe and Cisterns practice module to revise formulas, avoid common mistakes and improve accuracy in the CET 2026 Quant section.
