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 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 line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Choose the correct answer from the alternatives given.
Water is flowing at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank which is $50$ m long, $44$ m wide. The time taken (in hours) for the rise in the level of water in the tank to be $7$ cm is

  1. $2$
  2. $1\dfrac{1}{2}$
  3. $3$
  4. $2\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Water
flowed by the pipe in lh = $\pi r^2h$
= $\dfrac{22}{7} \times$ $\dfrac{7\times 7}{100\times100}$ $\times 5000 m^3 =77m^3$
Volume
of expected water in the tank = $\frac{50 \times 44 \times 7}{100} = 154
m^3$ 
Required
time= $154/77 = 2 hrs$.

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 ratio, proportion and unitary method more on proportion terms related to proportion proportion

A leak in the bottom of a tank can empty the full tank in $6$ hours. An inlet pipe fills water at the rate of $4$ litres per minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in $8$ hours, then the capacity of the tank is:

  1. $5260$ L
  2. $5760$ L
  3. $5846$ L
  4. $6970$ L
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done by the inlet in 1 hour $= \dfrac{1}{6}.\dfrac{1}{4}=\dfrac{1}{24}$

Work done by inlet in 1 min $=\dfrac{1}{24}\times \dfrac{1}{60}$
                                           
                                              $=\dfrac{1}{1440}$

Volume of$ \dfrac{1}{1440}$ part$ = 4$ litres
Volume of whole = $(1440 \times 4)$litres=$5760$  litres

Multiple choice physics option b: engineering physics buoyancy floatation fluid pressure

The water flowing from a garden hose fills a container $ 3 \pi $ litre in one minute.Then speed of the water coming from that pipe with opening of radius 1 cm is 

  1. $ 4 ms^{-1} $
  2. $5 ms^{-1} $
  3. $ 1 ms^{-1} $
  4. $ 0.5 ms^{-1} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume flow rate is Q = 3 pi litres / minute = 3 pi * 10^-3 m^3 / 60 s = (pi / 20) * 10^-3 m^3/s. Also, Q = A * v = pi * r^2 * v, where r = 1 cm = 10^-2 m. Equating the two expressions: pi * (10^-2)^2 * v = (pi / 20) * 10^-3, which simplifies to v = 0.5 m/s.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Four taps can individually fill a cistern of water in $1$ hour, $2$ hours, $3$ hours and $6$ hours respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes?

  1. $20$
  2. $30$
  3. $35$
  4. $40$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$4$ taps individually fill a cistern of water in $1$ hour, $2$ hours, $3$ hours and $6$ hours.
Part of the cistern filled in one hour
$= \left (1 + \dfrac {1}{2} + \dfrac {1}{3} + \dfrac {1}{6}\right ) = 2$
$\Rightarrow$ Twice the capacity is full in $60$ min.
Therefore, cistern is full in $30$ min.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

  1. $15$
  2. $20$
  3. $27.5$
  4. $30$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x minute will be taken. In one minute A can fill the $\dfrac {1}{60}$ part of tanker and in one minute B can fill the $\dfrac {1}{40}$ part.
Both can fill in t
$\dfrac {t}{60}+\dfrac {t}{40}=1$
$t=\dfrac {60\times 40}{100}$
$t=24$
both can fill in one minute $\dfrac {1}{24}$ part of tanker.
$1=\left (\dfrac {x}{2}\right )\dfrac {1}{40}+\dfrac {x}{2}\left (\dfrac {1}{24}\right )$
$1=\dfrac {x}{80}+\dfrac {x}{48}$
$x=\dfrac {80\times 48}{128}=30$

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?

  1. 6 min

  2. 8 min

  3. 10 min

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Y closed pipe after a min .
Then part filled by (X+Y) in a min +Part filled by X in (18-x) 
So $a(\frac{1}{24}+\frac{1}{32})+(18-a)\frac{1}{24}= 1$
Multy by 96 
Or 4a+3a+72-4a=96
Or 3x=24
Or x=8 min

Multiple choice

Pipes A, B and C can fill a cistern in 6 hr, 12 hr and 18 hr, respectively. Another pipe D can empty it in 15 hr. In which of the following cases will the tank be filled in the least time?

  1. If B alone is opened.

  2. If A and D are opened together.

  3. If A, B and D are opened.

  4. If B, C and D are opened.

  5. If A, C and D are opened.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rates (per hour): A=1/6, B=1/12, C=1/18, D=-1/15. A: 1/6 (rate 0.166). B: 1/12 (rate 0.083). A+D: 1/6 - 1/15 = 5/30 - 2/30 = 3/30 = 1/10 (rate 0.1). A+B+D: 1/6 + 1/12 - 1/15 = 10/60 + 5/60 - 4/60 = 11/60 (rate 0.183). B+C+D: 1/12 + 1/18 - 1/15 = 15/180 + 10/180 - 12/180 = 13/180 (rate 0.072). A+C+D: 1/6 + 1/18 - 1/15 = 15/90 + 5/90 - 6/90 = 14/90 (rate 0.155). The highest rate is A+B+D (11/60), which fills the tank in the least time.

Multiple choice

Two pipes A and B can fill a tank in 6 minutes and 7 minutes, respectively. If they are opened for one minute alternately, beginning with A, in how much time will they fill the tank?

  1. 7 minutes

  2. 65/8 minutes

  3. 61/8 minutes

  4. 63/7 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A fills 1/6 per min, B fills 1/7 per min. In 2 mins, they fill 1/6 + 1/7 = 13/42. In 6 mins (3 cycles), they fill 3 * 13/42 = 39/42. Remaining is 3/42 = 1/14. A fills 1/14 in (1/14) / (1/6) = 6/14 = 3/7 mins. Total time = 6 + 3/7 = 6 3/7 mins.