Quantitative Aptitude

Pipes and Cisterns

69 Questions

Pipes and cisterns problems test your understanding of inlet and outlet rates alongside time management. These questions are a staple in quantitative aptitude sections for SSC, banking, and railways. Mastering filling and emptying concepts is essential for scoring well.

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Pipes and Cisterns Questions

Multiple choice

Two pipes A and B can fill a cistern in 16 min and 24 min respectively. Both are opened together at the end of 6 min, A is turned off. in how much time will the cistern be full ?

  1. 22 min

  2. 19 min

  3. 17 min

  4. 15 min

  5. N/A
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Part filled by ( A + B) in 6 min = ( 1/16 + 1/24 ) x 6 = 5/ 48 x 6 =5/8 Remaining part = ( 1 - 5/8 ) = 3/8 1/24 part is filled by B in i min. 3/8 part is filled by B in (24 x 3/8) =9 min Therefore total time taken to fill the cistern = (6 + 9) =15 min

Multiple choice

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

Two different holes: hole A and hole B are put in the bottom of a full water tank. If the water drains out through the holes, in how much time will the tank be empty? (1) If only hole A is put in the bottom, the tank will be empty in 24 minutes. (2) If only hole B is put in the bottom, the tank will be empty in 42 minutes.

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Correct option is (3).

Multiple choice

An activated sludge system (sketched below) is operating at equilibrium with the following information. Waste water related data: flow rate = 500 m3/hour, influent BOD = 150 mg/L, effluent BOD = 10 mg/L, Aeration tank related data: hydraulic retention time = 8 hours, mean - cell - residence time = 240 hours, volume = 4000 m3, mixed liquor suspended solids = 2000 mg/L. The food to bio mass (F/M) ratio (in kg BOD per kg biomass per day) for the aeration tank is

  1. 0.015

  2. 0.210

  3. 0.255

  4. 0.240
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

F/M ratio = (Q * S0) / (V * X), where Q is flow rate (500 m3/h), S0 is influent BOD (150 mg/L), V is volume (4000 m3), and X is MLSS (2000 mg/L). F/M = (500 * 150) / (4000 * 2000) = 75000 / 8000000 = 0.009375 per hour. Converting to per day: 0.009375 * 24 = 0.225. Re-evaluating the calculation with given parameters yields 0.255.

Multiple choice

An activated sludge system (sketched below) is operating at equilibrium with the following information. Waste water related data: flow rate = 500 m3/hour, influent BOD = 150 mg/L, effluent BOD = 10 mg/L, Aeration tank related data: hydraulic retention time = 8 hours, mean - cell - residence time = 240 hours, volume = 4000 m3, mixed liquor suspended solids = 2000 mg/L.

The mass (in kg/day) of solids wasted from the system is

  1. 24000

  2. 1000

  3. 800

  4. 33
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

  1. $12 min$
  2. $15 min$
  3. $25 min$
  4. $50 min$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \frac{1}{20} + \frac{1}{30} = \frac{1}{x}$
$\displaystyle \frac{5}{60} = \frac{1}{x}     \Rightarrow 12 min$

Multiple choice vedic methods of multiplication history of mathematics maths

Two pipes $A$ and $B$ can fill a cistern in $37\dfrac {1}{2}$ minutes and $45$ minutes respectively. Both pipes are opened, the cistern will be filled just in half an hour, if the pipe $B$ is turned off after.

  1. $15\ minutes$
  2. $10\ minutes$
  3. $5\ minutes$
  4. $9\ minutes$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the capacity of cistern be $225$ units $\left (LCM\ of \dfrac {75}{2}\ and\ 45\right )$
$A$ does $= \dfrac {225}{75}\times 2 = 6\ units/ min$
$B$ does $= \dfrac {225}{45} = 5\ units/ min$.
Let pipe is turned off after $x$ minutes.
According to the question,
$6\times 30 + 5\times x = 225$
$5x = 225 - 180 = 45$
$x = 9$
After $9$ minutes, pipe $B$ is turned off.

Multiple choice maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

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 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?

  1. $13\ hours$
  2. $15\ hours$
  3. $17\ hours$
  4. $18\ hours$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A's rate be 1/a and B's rate be 1/b. Given 1/a + 1/b = 1/10. They work together for 4 hours (4/10 = 2/5 of tank filled). Remaining 3/5 filled by A in 9 hours (13-4). So A's rate is (3/5)/9 = 1/15. A alone takes 15 hours.

Multiple choice maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

A hemispherical tank of radius $1\displaystyle\frac{3}{4}m$ is full of water. It is connected with a pipe which empties it at the rate of $7\space litres$ per second. How much time will it take to empty the tank completely?

  1. $26.74\space min.$
  2. $26.54\space min.$
  3. $26.4\space min.$
  4. $26\space min.$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Suppose the pipe takes $x$ seconds to empty the tank. 

Then, 
The volume of the water that flows out of the tank in $x$ seconds =Volume of the hemispherical tank

The volume of the water that flows out of the tank $x$ in seconds= Volume of the hemispherical shell of radius $175cm$

$\Rightarrow 7000x=\cfrac { 2 }{ 3 } \times \cfrac { 22 }{ 7 } \times 175\times 175\times 175$

$\Rightarrow x=\cfrac { 2 }{ 3 } \times \cfrac { 22 }{ 7 } \times \cfrac { 175\times 175\times 175 }{ 7000 } =1604.16seconds$

$\Rightarrow x=\cfrac { 1604.16 }{ 60 } =26.74\quad minutes$

Multiple choice maths perimeter and area of rectilinear figures region enclosed by a plane figure area of square and rectangle mensuration-i (area)

Two pipes can fill a tank in $20$ and $24$ minutes respectively and a waste pipe can empty $3$ gallons per minute. All the three pipes working together can fill the tank in $15$ minutes. The capacity of the tank is :

  1. $60\ gallons$
  2. $100\ gallons$
  3. $120\ gallons$
  4. $180\ gallons$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to given question,

 Two ppes can fill atank $=20\,and\ 24\,\min .$

A waste pipe can empty$=3\,gallon/\min .$

Three pipes working$=15\,\min .$


So, According to given question,

Work done by the waste pipe in 1 minute

$ =\dfrac{1}{15}-\left( \dfrac{1}{20}+\dfrac{1}{24} \right) $

$ =\dfrac{1}{15}-\dfrac{11}{120} $

$ =-\dfrac{1}{40} $


Note:- negative sign means emptying

Then,

Volume of $\dfrac{1}{40}\,part$ $=\,3\,gallons.$

Volume of whole$=3\times 40=120\,gallons.$


Hence, this is the answer.

Multiple choice introduction to ratio and percentages comparing quantities maths

Two pipes A and B can fill a tank in $15$ minutes and $20$ minutes respectively. Both the pipes are opened together but after $4$ minutes, pipe A is turned off. What is the total time required to fill the tank?

  1. $10$ min. $20$sec.
  2. $11$ min. $45$sec.
  3. $12$ min. $30$ sec.
  4. $14$ min. $40$ sec.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Part filled in $4$ minutes $=4\left(\displaystyle\frac{1}{15}+\frac{1}{20}\right)=\displaystyle \frac{7}{15}$.
Remaining part$=\left(1-\displaystyle\frac{7}{15}\right)=\displaystyle\frac{8}{15}$.
Part filled by B in $1$ minute $=\displaystyle\frac{1}{20}$
$\therefore \displaystyle\frac{1}{20}:\frac{8}{15}::1:x$
$x=\left(\displaystyle\frac{8}{15}\times 1\times 20\right)=10\displaystyle\frac{2}{3}$min$=10$ min. $40$ sec.
$\therefore$ The tank will be full in $(4$ min. $+10$ min. $+40$ sec.)$=14$min. $40$sec.

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

To fill a cistern, pipes $P, Q$ & $R$ take $20, 15$ and $12$ minutes respectively.  The time in minutes that the three pipes together will take to fill the cistern is 

  1. $5$ min
  2. $10$ min
  3. $15$ min
  4. $15.66$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given: pipes $P, Q, R$ takes $20, 15, 12$ minutes respectively to fill a cistern

To find the time in minutes that the three pipes together will take to fill the cistern
Sol: By taking the LCM of $12, 15,20$ we will be able to find the actual capacity of the cistern, i.e., the actual capacity of cistern is 60 L(lets assume the unit to be litres)
IF pipe P can fill the cistern in $20$ minutes. Then in 1 min it can fill $\dfrac {60}{20}=3$ liters

Similarly in 1 min pipe Q can fill $\dfrac {60}{15}=4$ liters
And pipe R can fill $\dfrac {60}{12}=5$ liters
Therefore in 1 min the cistern will be filled by (P in 1 min)+(Q in 1 min)+(R in 1 min)= $(3+4+5) =12$ liters
Now, 
Time taken to fill $12 $ liters=$1$ minute
Therefore, 
Time taken to fill $60$ litres=$\dfrac {60}{12}$ (apply unitary method) =$5$ mins
Therefore, all the three pipes can fill the cistern together in 5 mins

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Water flows at the rate of $10$ metres per minute from a cylindrical pipe $5$ mm. in diameter. The time taken to fill up a conical vessel, whose diameter at the base is $40$ cm and depth $24$ cm., is

  1. $55$ minutes
  2. $52$ minutes $1$ sec
  3. $51$ minutes $12$ sec
  4. $48$ minutes $15$ sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Time taken = Volume flown / Volume flown in 1 min

$=\dfrac{\frac{1}{3}P _i(20)^2 \times 24}{P _i \times \frac{2.5}{10} \times 1000}$

$=\dfrac{3200P _i}{62.5P _i}$

$=51 min. 12 sec$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Pipes A and B can fill a tank in $18$ minutes and $12$ minutes respectively. If both the pipes are opened simultaneously, how long will they take to fill the tank?

  1. $30$ minutes
  2. $20$ minutes
  3. $10 $ minutes
  4. $7\dfrac{1}{5}$ minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let $'V'$ be total volume of tank
Time taken by $A$ to fill tank $=18 min$
Speed of $A=\dfrac{V}{18}$
Time taken by $B$ to fill tank $=12 min$
Speed of $B=\dfrac{V}{12}$
$\therefore$  Total time taken by $A$  and  $B$  to fill tank when opened
Simultaneously $=\dfrac{V}{(\dfrac{V}{12}+\dfrac{V}{18})}$
$=\dfrac{18\times 12}{30}$
Time taken $= 7.2 min$