Pipe and Cistern MCQ Quiz - Objective Question with Answer for Pipe and Cistern - Download Free PDF
Last updated on Jun 12, 2025
Latest Pipe and Cistern MCQ Objective Questions
Pipe and Cistern Question 1:
A cistern has an inlet pipe and an outlet pipe. Inlet pipe can fill three-fourth of the cistern in 24 minutes while outlet pipe can empty the one-third filled cistern in 16 minutes. If both the pipes are opened together, then the cistern will be completely filled in-
Answer (Detailed Solution Below)
Pipe and Cistern Question 1 Detailed Solution
Given:
Inlet pipe can fill three-fourths of the cistern in 24 minutes.
Outlet pipe can empty one-third of the cistern in 16 minutes.
Calculations:
Rate of the inlet pipe = (3/4) cistern / 24 minutes = 3 / (4 × 24) = 1 / 32 cistern per minute.
Rate of the outlet pipe = (1/3) cistern / 16 minutes = 1 / (3 × 16) = 1 / 48 cistern per minute.
When both pipes are opened together, the combined rate is:
Combined rate = Rate of inlet pipe - Rate of outlet pipe = 1/32 - 1/48
To subtract, find the LCM of 32 and 48, which is 96:
1/32 = 3/96, and 1/48 = 2/96, so combined rate = (3/96) - (2/96) = 1/96 cistern per minute.
Thus, the cistern will be filled in 96 minutes.
∴ The cistern will be completely filled in 96 minutes.
Pipe and Cistern Question 2:
Pipe A can fill a tank in 816 minutes and Pipe B can empty the same tank in 1020 minutes. If both pipes are opened together, how many hours will it take to fill the empty tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 2 Detailed Solution
Given:
Pipe A can fill the tank in 816 minutes.
Pipe B can empty the tank in 1020 minutes.
Formula used:
Efficiency of Pipe A = 1 / 816 (since it fills the tank in 816 minutes)
Efficiency of Pipe B = -1 / 1020 (since it empties the tank in 1020 minutes)
Calculations:
When both pipes are opened together, the net efficiency is the sum of their efficiencies:
Net efficiency = (1 / 816) - (1 / 1020)
To calculate this, we first find the LCM of 816 and 1020, which is 8160:
Net efficiency = (10 / 8160) - (8 / 8160) = 2 / 8160
The time taken to fill the tank is the inverse of the net efficiency:
Time = 8160 / 2 = 4080 minutes
Convert this time into hours:
Time in hours = 4080 / 60 = 68 hours
∴ It will take 68 hours to fill the empty tank when both pipes are opened together.
Pipe and Cistern Question 3:
Pipe A can fill a tank in 780 minutes and Pipe B can empty the same tank in 975 minutes. If both pipes are opened together, how many hours will it take to fill the tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 3 Detailed Solution
Given:
Pipe A can fill the tank in 780 minutes
Pipe B can empty the tank in 975 minutes
Formula used:
Work = LCM of times taken
Efficiency = Work ÷ Time
Net work = Filling efficiency - Emptying efficiency
Time = Total work ÷ Net efficiency
Calculations:
LCM of 780 and 975 = 50700 units (Total work)
⇒ A’s 1 min work = 50700 ÷ 780 = 65 units
⇒ B’s 1 min work = 50700 ÷ 975 = 52 units
⇒ Net 1 min work = 65 - 52 = 13 units
⇒ Time = 50700 ÷ 13 = 3900 minutes
⇒ Convert to hours: 3900 ÷ 60 = 65 hours
∴ The tank will be filled in 65 hours.
Pipe and Cistern Question 4:
Pipe A can fill a tank in 105 minutes, Pipe B can fill the same tank in 63 minutes and Pipe C can empty the same tank in 42 minutes. If all three pipes are opened together, how many minutes will it take to fill the empty tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 4 Detailed Solution
Given:
Pipe A fills the tank in 105 minutes.
Pipe B fills the tank in 63 minutes.
Pipe C empties the tank in 42 minutes.
Formula used:
Time is taken to fill the tank = XYZ / (YZ + XZ -XY)
where X, Y, and Z are time taken by Pipe A, B, and C respectively.
Calculation:
Applying the above formula
Time taken to fill the tank = (105 × 63 × 42) / ( 63 × 42 + 105 × 42 - 105 × 63)
= 277830 / 441
= 630 minutes
∴ The correct answer is 630 minutes.
Pipe and Cistern Question 5:
Pipe A can fill a tank in 165 minutes, Pipe B can fill the same tank in 99 minutes and Pipe C can empty the same tank in 66 minutes. If all three pipes are opened simultaneously, how many minutes will it take to fill the empty tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 5 Detailed Solution
Given:
Pipe A can fill the tank in 165 minutes.
Pipe B can fill the tank in 99 minutes.
Pipe C can empty the tank in 66 minutes.
Formula used:
Efficiency of a pipe = 1 / Time taken by the pipe to fill/empty the tank
Let the total work be the LCM of 165, 99, and 66.
Calculations:
Let the capacity of the tank is = LCM of 165, 99, and 66 = 495
Efficiency of Pipe A = 495 / 165 = 3 (filling per minute)
Efficiency of Pipe B = 495 / 99 = 5 (filling per minute)
Efficiency of Pipe C = 495 / 66 = -7.5 (emptying per minute)
Net efficiency = 3 + 5 - 7.5 = 0.5 (filling per minute)
Time to fill the tank = Total work / Net efficiency = 495 / 0.5 = 990 minutes
∴ It will take 990 minutes to fill the tank when all three pipes are opened simultaneously.
Top Pipe and Cistern MCQ Objective Questions
A cistern has two pipes one can fill it with water in 16 hours and other can empty it in 10 hours. In how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?
Answer (Detailed Solution Below)
Pipe and Cistern Question 6 Detailed Solution
Download Solution PDFShortcut Trick
If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units
According to question,
Amount of water in the tank = (1/5) × 80 = 16 units
Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours
Alternate Method
GIVEN :
Time by which pipe A can fill the tank = 16 hours
Time by which pipe B can empty the tank = 10 hours
The cistern is (1/5)th full.
CONCEPT :
Total work = time × efficiency
CALCULATION :
Work | Time | Efficiency |
A | 16 | 80/16 = 5 |
B | 10 | 80/10 = (-8) |
total work (LCM) |
80 |
Negative efficiency indicates pipe B is emptying the tank.
If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units
From the total efficiency it is clear that when both are opened, the tank is being emptied.
Amount of water in the tank = (1/5) × 80 = 16 units
The water level will not rise as the total action is emptying when both are opened together.
Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours
∴ Time taken to empty the tank is 5.33 hours.
Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?
Answer (Detailed Solution Below)
Pipe and Cistern Question 7 Detailed Solution
Download Solution PDFGiven:
First pipe can fill the cistern = 3 hours
Second pipe can fill the cistern = 4 hours
Third pipe can drain the cistern = 8 hours
Calculation:
Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)
Work done by pipe 1 in 1 hour = 24/3 = 8 units.
Work done by pipe 2 in 1 hour = 24/4 = 6 units.
Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units
Total work done in 1 hour = 8 + 6 – 3 = 11 units
The time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours
∴ The correct answer is 2 hours.
An inlet pipe can fill an empty tank in \(4\frac{1}{2}\) hours while an outlet pipe drains a completely filled tank in \(7\frac{1}{5}\) hours. The tank is initially empty. and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled?
Answer (Detailed Solution Below)
Pipe and Cistern Question 8 Detailed Solution
Download Solution PDFGiven:
An inlet pipe can fill an empty tank in \(4\frac{1}{2}\) hours while an outlet pipe drains a completely filled tank in \(7\frac{1}{5}\) hours.
Concept used:
Efficiency = (Total work / Total time taken)
Efficiency = work done in a single day
Calculation:Time taken by A = 9/2 hours
Please note that after 20 hours, the remaining capacity = 6 units
Now in the 21st hour, pipe A will work and fill the tank so no need to add time after that.
Time taken by pipe A to fill 6 units = 6/8 = 3/4 hours
So,
Pipes A and B can fill a tank with water in 30 minutes and 40 minutes, respectively, while pipe C can drain off 51 litres of water per minute. If all the three pipes are opened together, the tank is filled in 90 minutes. What is the capacity (in litres) of the tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 9 Detailed Solution
Download Solution PDFGiven:
Pipes A can fill a tank with water in 30 minutes
Pipes B can fill a tank with water in 40 minutes
Pipe C can drain off 51 litres of water per minute
All the three pipes are opened together, the tank is filled in 90 minutes
Concept used:
LCM method used,
Calculation:
According to the question:
Lcm of (30, 40, 90) = 360
Efficiency of C = (12 + 9) - 4 = 17 l/min
Which is actually 51 litres/min,
⇒ 17 unit = 51lit
⇒ 360 unit = (51/17) × 360 = 1080 litres
∴ The capacity (in litres) of the tank is 1080 litres.
Both tap M and tap N together can fill a tank in 20/3 hours. If tap M opens for only 4 hours and the remaining tank is filled by tap N for only 9 hours. How many hours to fill the tank by tap N?
Answer (Detailed Solution Below)
Pipe and Cistern Question 10 Detailed Solution
Download Solution PDFCalculation:
According to question
⇒ (M + N) × 20/3 = 4M + 9N
⇒ 20M + 20N = 12M + 27N
⇒ 8M = 7N
⇒ M/N = 7/8
To fill the complete tank by tap N = (4M + 9N)/efficiency of N
To fill the complete tank by tap N = (4 × 7 + 9 × 8)/8 = 100/8 = 25/2
∴ To fill the complete tank by tap N is 12.5 hoursTwo pipes can fill a cistern separately in 20 minutes and 40 minutes respectively and a waste pipe can drain off 35 gallons per minute. If all three pipes are opened, the cistern gets filled in an hour. What is the capacity of the cistern?
Answer (Detailed Solution Below)
Pipe and Cistern Question 11 Detailed Solution
Download Solution PDFCalculation:
Let capacity of cistern be x gallons
Pipe A fills cistern in 20 min
⇒ Cistern filled by pipe A in 1 hour = 3x
Pipe B fills cistern in 40 min
⇒ Cistern filled by pipe B in 1 hour = 60/40 = 1.5x
⇒ Water drained by waste pipe in 1 hour = 35 × 60 = 2100 gallons
If all three pipes are connected, Cistern fills in 1 hour
⇒ 3x + 1.5x - 2100 = x
⇒ 4.5x - x = 2100
⇒ 3.5x = 2100
⇒ x = 2100/3.5 = 600
∴ The correct answer is 600 gallons
Alternate Method Let's denote the capacity of the cistern as C gallons. We then have:
The rate of the first pipe is C/20 gallons per minute.
The rate of the second pipe is C/40 gallons per minute.
The waste pipe drains at a rate of 35 gallons per minute.
When all three pipes are open, the cistern is filled in 60 minutes (1 hour), meaning the net rate is C/60 gallons per minute.
(C/20) + (C/40) - 35 = C/60
6C + 3C - 4200 = 2C
7C = 4200
C = 4200 / 7 = 600
So, the capacity of the cistern is 600 gallons.
Working together, pipes A and B can fill an empty tank in 10 hours. They worked together for 4 hours and then B stopped, and A continued filling the tank till it was full. It took a total of 13 hours to fill the tank. How long would it take A to fill the empty tank alone?
Answer (Detailed Solution Below)
Pipe and Cistern Question 12 Detailed Solution
Download Solution PDFCalculation:
Working together, pipes A and B can fill an empty tank in 10 hours,
⇒ 1/A + 1/B = 1/10
together they worked for 4 hours and then A continued, and work completed in 13 hrs,
It means A worked for 13 hrs.
⇒ (4/A + 4/B) + 9/A = 1
⇒ 4/10 + 9/A = 1
∴ A = 15 hrs
Alternate Method
Time is taken to fill the tank by A and B = 10 hrs = 100% of total work
A and B worked together for 4 hrs = 40% of total work
So, 6 hours of work remaining = 60% of total work
Work done by A alone = 13 - 4 = 9 hours
60% of work is done by A in 9 hours
100% of work = (9/60) × 100 = 15 hours
∴ The time taken by A to complete work is 15 hours.
Taps P, Q, and R can fill a tank in 20, 25, and 40 hours respectively. Taps Q is kept open for 10 hours, and then tap Q is closed, after that tap P and R are opened. Tap R is closed 9 hours before the tank overflows. How long does it take to fill the tank?
Answer (Detailed Solution Below)
Pipe and Cistern Question 13 Detailed Solution
Download Solution PDFGiven:
Tap P can fill a tank = 20 hours
Tap Q can fill a tank = 25 hours
Tap R can fill a tank = 40 hours
Calculation:
Let the total work be LCM of 20, 25, and 40 = 200 units
⇒ Efficiency of tap P = 200/20 = 10 units
⇒ Efficiency of tap Q = 200/25 = 8 units
⇒ Efficiency of tap R = 200/40 = 5 units
Since the tap Q is kept open for 10 hours,
Work done by tap Q = 10 × 8 = 80 units
∵ Tap R is closed 9 hours before the tank overflows
⇒ Tap P alone worked for 9 hours.
⇒ Work done by tap P alone = 9 × 10 = 90 units
Remaining work = 200 - (80 + 90) = 30 units
The remaining work was done by tap P and tap R together
Time taken by tap P and Tap R to complete the remaining work = 30/(10 + 5) = 30/15 = 2 hours
∴ The total time to fill the tank is (10 + 9 + 2) 21 hours.
Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 8 hours. Pipe A, B and C together can fill the same tank in 12 hours. Then which of the following statements is true for pipe C?
Answer (Detailed Solution Below)
Pipe and Cistern Question 14 Detailed Solution
Download Solution PDFGiven:
Time taken by A to fill tank = 6 hours
Time taken by B to fill tank = 8 hours
Time taken by A, B and, C together to fill the tank = 12 hours
Concept used:
Total work = time × efficiency
Calculation:
Let the capacity of the tank ( work to be done) be 24x units (LCM of 6, 8, 12)
⇒ The efficiency of pipe A = 24x/6 = 4x units/day
⇒ Efficiency of pipe B = 24x/8 = 3x units/day
⇒ Efficiency of pipe (A + B + C) = 24x/12 = 2x units/day
⇒ Efficiency of pipe C = efficiency of (A + B = C) - efficiency of (A + B)
Efficiency of pipe C = 2x – (4x + 3x) = – 5x units/day
Negative efficiency implies that pipe C is emptying pipe.
⇒ Time taken by pipe C to empty the filled tank = 24x/5x
= 4.8 hours or 4 hrs 48 min
∴ The pipe C will empty the tank in 4 hrs 48 mins.
Pipe A and pipe B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill it, then the time in which A and B will fill that cistern separately will be, respectively, __________ .
Answer (Detailed Solution Below)
Pipe and Cistern Question 15 Detailed Solution
Download Solution PDFGiven:
Pipe A and pipe B running together can fill a cistern in 6 minutes.
B takes 5 minutes more than A to fill it.
Concept used:
Efficiency = (Total work / Total time taken)
Efficiency = work done in a single day
Calculation:
Let Pipe A takes x minutes
So pipe B takes x+5 minutes
As per the question,
1/x + 1/(x+5) = 1/6
2x + 5 = x(x+5) 1/6
12x + 30 = x2 + 5x
x2 - 7x - 30 = 0
(x+3)(x-10) = 0
So x = 10
Time taken by B is 10 + 5 = 15 minutes
∴ The correct option is 4