Pipes and Cisterns Quiz Set 001

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Question 1

Tap M can fill a cistern in 16 mins. And, a tap N can empty it in 11 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is $7/15$th already empty?

 A

$18{58/75}$ mins.

 B

$20{3/74}$ mins.

 C

$17{24/77}$ mins.

 D

$21{16/77}$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in ${16 × 11}/{16 - 11}$ mins. So $1 - 7/15$ = $8/15$ filled cistern can be emptied in ${16 × 11}/{16 - 11}$ × $8/15$ = ${1408/75}$, which is same as: $18{58/75}$ mins.


Question 2

Two pipes can together fill a cistern in 4 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

 A

20 mins.

 B

21 mins.

 C

19 mins.

 D

22 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 4 × $(1/x + 4/x)$ = 1. Solving for x, we get x = 4 × 5 = 20 mins.


Question 3

Two taps X, Y and Z can fill a tank in 18, 17 and 10 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

 A

$4{109/164}$ mins.

 B

$5{114/163}$ mins.

 C

$3{103/166}$ mins.

 D

$7{95/166}$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. $x/18 + x/17 + x/10 = 1$. Solving, we get x = $4{109/164}$. Or use the shortcut ${abc}/{ab + bc + ca}$. Another thing, instead of solving the entire calculation, you can keep an eye on the options to find the nearest answer.


Question 4

Tap X can fill the tank in 19 mins. Tap Y can empty it in 6 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is $13/17$th full of water?

 A

$6{12/17}$ mins.

 B

$8{3/16}$ mins.

 C

$5{2/19}$ mins.

 D

$8{13/19}$ mins.

Soln.
Ans: a

1 filled tank can be emptied in ${19 × 6}/{19 - 6}$ mins. So 13/17 can be emptied in ${19 × 6}/{19 - 6}$ × $13/17$ = ${114/17}$, which is same as: $6{12/17}$ mins.


Question 5

Three taps R, G and B are supplying red, green and blue colored inks into a tub. They can independently fill the tub in 6, 2 and 8 minutes. They are turned on at the same time. What is the ratio of blue ink after 3 minutes?

 A

${3/19}$.

 B

$1{2/9}$.

 C

${1/7}$.

 D

$2{6/7}$.

Soln.
Ans: a

Let the time taken by them to independently fill the tank be r, g and b minutes. Ink discharged by the blue tap is $3/b$. The total of all the inks is $3/r + 3/g + 3/b$. The ratio is ${1/b}/{1/r + 1/g + 1/b}$, which simplifies to ${rg}/{rg + gb + br}$ = ${3/19}$.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer


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