Quantitative Aptitude

Pipes and Cisterns

535 Questions
All Delayed opening or closing 106 Combined pipes and the LCM shortcut 77 Find unknown pipe time 64 Efficiency ratios and faster-pipe relations 61 Flow rates based on pipe diameter 50 Leaks and reverse-rate questions 50 Actual capacity and pump-rate equations 44 Partial filling or emptying condition 44 Alternating pipes and changing phases 39

Pipes and Cisterns Questions

Multiple choice

Two pipes can fill a cistern in 30 and 15 h respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom 5 h extra are taken for cistern to be filled up. If the cistern in full in what time would the leak empty it ?

  1. 10 hours

  2. 20 hours

  3. 30 hours

  4. 40 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipes fill at 1/30 + 1/15 = 1/10 per hour. With leak, rate is 1/10 - 1/L. Time taken is 10 + 5 = 15 hours. So 1/10 - 1/L = 1/15. 1/L = 1/10 - 1/15 = 1/30. L = 30 hours.

Multiple choice

A cistern can be filled by two pipes in 30 and 40 min respectively. Both the pipes are opened at once, when the first pipe must be turned off so that the tank may be just filled in 18 min ?

  1. 12.5 min

  2. 13.5 min

  3. 14.5 min

  4. 16.5 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the first pipe be open for x minutes. Pipe 1 rate = 1/30, Pipe 2 rate = 1/40. Pipe 2 is open for 18 minutes. Equation: x/30 + 18/40 = 1. x/30 = 1 - 18/40 = 22/40 = 11/20. x = 30 * 11/20 = 33/2 = 16.5 minutes.

Multiple choice

Pipe A fills a tank of $700$ litres capacity at the rate of $40$ litres a minute. Another pipe B fills the same tank at the rate of $30$ litres a minute. A pipe at the bottom of the tank drains the tank at the rate of $20$ litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?
  1. $42$ minutes
  2. $30$ minutes
  3. $12$ minutes
  4. $4$ minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Two pipes A and B can fill a cistern in $\displaystyle 37\frac{1}{2}$ min and $45$ min respectively. Both pipes were opened and the cistern was filled in just $\displaystyle \frac{1}{2}$ an hour if the pipe B is turned off after what time it is opened?
  1. $5$ min
  2. $9$ min
  3. $10$ min
  4. $15$ min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fills 1/37.5 = 2/75 per min. B fills 1/45 per min. If B is turned off after t minutes, A works for 30 mins. (2/75)*30 + (1/45)*t = 1. 4/5 + t/45 = 1. t/45 = 1/5. t = 9 minutes.

Multiple choice

An empty tank is connected with pipes A, B and C. A and B inlet pipes and they fill the tank in $6$ hours and $8$ hours respectively. While C is an outlet pipe and it empties the completely filled tank in $5$ hours. Find the time in which the tank will be completely filled if all the pipes are opened together.
  1. $\dfrac{119}{11}$ hours
  2. $\dfrac{108}{11}$ hours
  3. $\dfrac{120}{11}$ hours
  4. $\dfrac{109}{11}$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rates: A = 1/6, B = 1/8, C = -1/5. Combined rate = 1/6 + 1/8 - 1/5 = (20 + 15 - 24) / 120 = 11/120. Time = 120/11 hours.

Multiple choice

Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to $\displaystyle \frac { 1 }{ 2 } $ of capacity in 3 hours and a second inlet pipe fills the same empty tank to $\displaystyle \frac { 2 }{ 3 } $ of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

  1. 3.25

  2. 3.6

  3. 4.2

  4. 4.4

  5. 5.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe 1 fills 1/2 in 3 hours, so it fills 1/6 per hour. Pipe 2 fills 2/3 in 6 hours, so it fills 1/9 per hour. Combined rate = 1/6 + 1/9 = 3/18 + 2/18 = 5/18 per hour. Time to fill = 1 / (5/18) = 18/5 = 3.6 hours.

Multiple choice

A water tank has two pipes to fill it. Pipe A can fill the tank in $2$ hours , only if tank is empty. Pipe B can empty the tank in $3$ hours, only if tank is full. If both the pipes start at the same time when the task is empty, calculate the number of hours will it take for the tank to be filled to $60\%$ of its capacity?
  1. $2.4$
  2. $3.6$
  3. $6$
  4. $60$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rate A = 1/2 tank/hr. Rate B = -1/3 tank/hr. Combined rate = 1/2 - 1/3 = 1/6 tank/hr. To fill 60% (0.6) of the tank: Time = 0.6 / (1/6) = 3.6 hours.

Multiple choice

Choose the correct answer from the alternatives given : Two taps can separately fill a cistern in $20$ and $30$ minutes respectively. Each of the taps is opened for a minute in turn, but due to a hole at the bottom of the cistern and discharge of the water through that, it takes $3$ minutes more to fill the cistern. If the cistern is full of water, find the time taken by the hole to empty it.
  1. $2\frac {4}{7}$ hours
  2. $5\frac {1}{3}$ hours
  3. $3\frac {3}{5}$ hours
  4. $4\frac {1}{3}$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Two pipes can fill an empty tank separately in $24$ minutes and $40$ minutes respectively and a third pipe can empty $30$ gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is
  1. $500$
  2. $550$
  3. $600$
  4. $700$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let C be the capacity. The rates of the three pipes are C/24, C/40, and -30. Combined, they fill the tank in 60 minutes: C/24 + C/40 - 30 = C/60. Solving for C: C(1/24 + 1/40 - 1/60) = 30, which simplifies to C(5/120 + 3/120 - 2/120) = 30, or C(6/120) = 30, so C = 600.

Multiple choice

Two pipes can fill a cistern separately in $24\ min$ and $40\ min$ respectively. Waste pipe is opened which can drain the cistern at $30\ liters/ minute$. If all the pipe are opened together then the cistern fills in one hour. The capacity (in litre) of the cistern is?
  1. $800$
  2. $400$
  3. $600$
  4. $500$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let capacity be C. Pipe A fills at C/24, Pipe B at C/40. Waste pipe drains at 30 L/min. In 60 mins, (C/24 + C/40 - 30) * 60 = C. (5C/120 + 3C/120 - 30) * 60 = C. (8C/120 - 30) * 60 = C. (C/15 - 30) * 60 = C. 4C - 1800 = C. 3C = 1800, C = 600.