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

A cistern can be filled up by one pipe in 12 hours and by another in 8 hours. Both the pipes are kept open for $2\displaystyle\frac{1}{2}$ hours. The part of the cistern filled up is
  1. $\displaystyle\frac{25}{48}$
  2. $\displaystyle\frac{5}{6}$
  3. $\displaystyle\frac{25}{36}$
  4. $\displaystyle\frac{12}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe 1 rate = 1/12 per hour. Pipe 2 rate = 1/8 per hour. Combined rate = 1/12 + 1/8 = 2/24 + 3/24 = 5/24 per hour. In 2.5 (5/2) hours, the filled part is (5/24) * (5/2) = 25/48.

Multiple choice

A pipe can fill a tank in $x$ hours and another pipe can empty it in $y\left( y>x \right)$ hours. If both the pipes are open, in how many hours will the tank be filled?
  1. $\left( x-y \right)$
  2. $\left( y-x \right)$
  3. $\displaystyle\frac { xy }{ \left( x-y \right) }$
  4. $\displaystyle\frac { xy }{ \left( y-x \right) }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rate of filling pipe = 1/x. Rate of emptying pipe = 1/y. Combined rate = 1/x - 1/y = (y - x) / xy. Time taken = 1 / (combined rate) = xy / (y - x).

Multiple choice

Two pipes $A$ and $B$ can separately fill a cistern in $60\ minutes$ and $75\ minutes$ respectively. There is a third pipe at the bottom of the cistern to empty it , If all the three pipes are simultancously opened, then the cistern is full in $50\ minutes$, In how much time, the third pipe alone can empty the cistern ?
  1. $110\ minutes$
  2. $100\ minutes$
  3. $120\ minutes$
  4. $90\ minutes$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the capacity be 300 units. A fills 5 units/min, B fills 4 units/min. Together they fill 9 units/min. With the third pipe C, they fill 300/50 = 6 units/min. So C empties 9 - 6 = 3 units/min. Time for C = 300 / 3 = 100 minutes.

Multiple choice

Two pipes A and B together can fill a cistern in $4$ hours. Had they been opened separately, then B would have taken $6$ hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
  1. $1$ hour
  2. $2$ hours
  3. $6$ hours
  4. $8$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A take x hours, then B takes x + 6 hours. Together, 1/x + 1/(x+6) = 1/4. Solving 4(x+6 + x) = x(x+6) gives 8x + 24 = x^2 + 6x, or x^2 - 2x - 24 = 0. Factoring gives (x-6)(x+4) = 0. Since time is positive, x = 6.

Multiple choice

A tank is filled in $5$ hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A lone take to fill the tank?
  1. $20$ hours
  2. $25$ hours
  3. $35$ hours

  4. Cannot be determined

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

Let pipe A's rate be x. Then B works at 2x and C at 4x, so the combined rate is 7x. Since the tank fills in 5 hours, 7x = 1/5, giving x = 1/35. Pipe A alone therefore takes 35 hours.

Multiple choice

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank $5$ hours faster than the first pipe and $4$ hours slower than the third pipe. The time required by the first pipe is.
  1. $6$ hours
  2. $10$ hours
  3. $15$ hours
  4. $30$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the rates of the pipes be 1/x, 1/(x-5), and 1/(x-9). The problem states the rate of the third pipe equals the sum of the first two: 1/(x-9) = 1/x + 1/(x-5). Solving this quadratic equation x^2 - 19x + 45 = 0 leads to x = 15 as the valid solution.

Multiple choice

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is$/$are necessary to answer the question. If both the pipes are opened, how many hours will be taken to fill the tank? I. The capacity of the tank is $400$ litres. II. The pipe A fills the tank in $4$ hours. III. The pipe B fiils the tank in $6$ hours.

  1. Only I and II

  2. Only II and III

  3. All I, II and III

  4. Any two of the three

  5. Even with all the three statements, answer cannot be given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the time taken by two pipes together, we need their individual rates. Statement II gives pipe A's rate, and Statement III gives pipe B's rate. Statement I is redundant as the capacity cancels out.

Multiple choice

Two pipes A and B can fill a tank in $24$ and $30$ minutes respectively. Both are turned on together. But at the end of $8$ minutes, the first is turned off. The time taken to fill the tank B is
  1. $10\ min.$
  2. $8\ min.$
  3. $12\ min.$
  4. $16\ min.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills 1/24 per min, B fills 1/30 per min. In 8 mins, A and B fill 8 * (1/24 + 1/30) = 8 * (5/120 + 4/120) = 8 * 9/120 = 72/120 = 3/5. Remaining tank = 2/5. Pipe B fills 2/5 at 1/30 rate: (2/5) / (1/30) = 12 minutes.

Multiple choice

Two pipes A and B can fill a tank in $4$ hours and $5$ hours respectively. If they are turned up alternatively for one hour each, the time taken to fill the tank is
  1. $2\ hrs\ 15\ min$
  2. $4\ hrs\ 24\ min$
  3. $5\ hrs$
  4. $3\ hrs$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/4 of the tank per hour, and Pipe B fills 1/5 per hour. In two hours (one hour each), they fill 1/4 + 1/5 = 9/20 of the tank. After 4 hours, they have filled 18/20 = 9/10 of the tank, leaving 1/10 to be filled by Pipe A, which takes 1/10 / (1/4) = 0.4 hours or 24 minutes.

Multiple choice

A cistern has a leak which would empty it in $8$ hours. A tap is turned on which admits $6$ litres a minute into the cistern and is now emptied in $12$ hours. How many litres does the cistern hold?
  1. $8640$
  2. $8500$
  3. $4320$
  4. $60\ hours$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the capacity be C. The leak empties at C/8 per hour. With the tap adding 6 liters/min (360 liters/hour), the net rate is C/12. So, C/8 - 360 = C/12. Solving for C: C/8 - C/12 = 360, which simplifies to C/24 = 360, so C = 8640 liters.

Multiple choice

Pipe A can fill a tank in $10h$ and pipe $B$ can fill the same tank in $12h$. Both the pipes are opened to fill the tank and after $3h$ pipe $A$ is closed. Pipe $B$ will fill the remaining part of the tank in
  1. $5h$
  2. $4h$
  3. $5h$ $24min$
  4. $3h$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: A = 1/10, B = 1/12. In 3 hours, A+B do 3 * (1/10 + 1/12) = 3 * (11/60) = 33/60 = 11/20. Remaining work = 9/20. B takes (9/20) / (1/12) = 9/20 * 12 = 108/20 = 5.4 hours, which is 5 hours 24 minutes.

Multiple choice

If a pipe can fill a cistern in 8 hours and another pipe can empty the cistern in 10 hours, then what part of the cistern will be filled in 1 hour, if both pipes are opened simultancously?
  1. $\frac { 1 }{ 40 } $
  2. $\frac { 1 }{ 30 } $
  3. $\frac { 1 }{ 35 } $
  4. $\frac { 1 }{ 8 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The filling rate is 1/8 of the cistern per hour, while the emptying rate is 1/10 per hour. Their net rate is 1/8 - 1/10 = 1/40 of the cistern per hour.