Pipes and Cisterns Quiz Set 018

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Question 1

Tap M can fill a cistern in 17 mins. And, a tap N can empty it in 15 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is $11/14$th already empty?

 A

$27{9/28}$ mins.

 B

$29{10/27}$ mins.

 C

$24{17/30}$ mins.

 D

$28{3/10}$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in ${17 × 15}/{17 - 15}$ mins. So $1 - 11/14$ = $3/14$ filled cistern can be emptied in ${17 × 15}/{17 - 15}$ × $3/14$ = ${765/28}$, which is same as: $27{9/28}$ mins.


Question 2

A tank is (5/9)th filled with water. When 9 liters of water are added, it becomes (2/3)th filled. What is the capacity of the tank?

 A

81 liters.

 B

91 liters.

 C

101 liters.

 D

111 liters.

Soln.
Ans: a

Let x be the capacity in liters. ${5x}/9 + 9 = {2x}/3$. Solving, x = 81 liters.


Question 3

One tap can fill a tank 4 times faster than the other. If they together fill it in 7 minutes, how much time does the slower alone take to fill the tank?

 A

35 mins.

 B

5 mins.

 C

3 mins.

 D

7 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 4/x. We have $1/x + 4/x = 1/7$, which gives x = 5 × 7 = 35 mins.


Question 4

A tank is filled in 16 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

 A

a3 - 48a2 - ad2 + 16d2 = 0.

 B

a3 - 32a2 + ad2 + 16d2 = 0.

 C

a3 - 16a2 - ad2 + 16d2 = 0.

 D

a3 - 80a2 + ad2 + 16d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 16 minutes work of all the taps should add to 1. So we have, $16 × 1/{a - d} + 16 × 1/a + 16 × 1/{a + d}$ = 1, which is same as a3 - 48a2 - ad2 + 16d2 = 0.


Question 5

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.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 018" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-10-26.

Posted by Parveen(Hoven),
Aptitude Trainer


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