Pipes and Cisterns Quiz Set 020

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Question 1

Two taps X, Y and Z can fill a tank in 5, 17 and 4 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

 A

$1{167/173}$ mins.

 B

$2{169/172}$ mins.

 C

${167/175}$ mins.

 D

$4{159/175}$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. $x/5 + x/17 + x/4 = 1$. Solving, we get x = $1{167/173}$. 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 2

Two pipes, A and B, can fill a cistern in 5 and 8 mins respectively. There is a leakage tap that can drain 8 liters of water per minute. If all three of them work together, the tank is filled in 15 minutes. What is the volume of the tank?

 A

$30{30/31}$ liters.

 B

$33{1/30}$ liters.

 C

$28{5/33}$ liters.

 D

$31{10/11}$ liters.

Soln.
Ans: a

Work done by the leakage in 1 min is $1/5 + 1/8 - 1/15$ = ${31/120}$. This work is equivalent to a volume of 8 liters. So, the total volume is 8 × ${120/31}$ = ${960/31}$, which is same as: $30{30/31}$ liters.


Question 3

A tank is filled in 19 minutes by three taps running together. Tap A is twice as fast as tap B, and tap B is twice as fast as tap C. How much time will tap A take to fill the tank?

 A

133 mins.

 B

134 mins.

 C

132 mins.

 D

135 mins.

Soln.
Ans: a

Let the time taken by tap A be x mins. Then 19 minutes work of all the taps should add to 1. So we have, $19 × 1/x + 19 × 2/x + 19 × 4/x$ = 1, which is same as $19 × 7/x$ = 1. Solving, we get x = 133 mins.


Question 4

A bucket can be filled by a tap in 6 minutes. Another tap on the same bucket can empty it in 15 mins. How long will it take to fill the bucket if both the taps are opened together?

 A

10 mins.

 B

11 mins.

 C

9 mins.

 D

$4{1/3}$ mins.

Soln.
Ans: a

Net part filling in one hour is $1/x - 1/y$ = $(y - x)/(xy)$. So complete filling occurs in $(xy)/(y - x)$ = ${6 × 15}/{15 - 6}$ = 10 mins.


Question 5

Two pipes can together fill a cistern in 7 minutes. How long does the slower alone take if the speeds of the pipes are in the ratio 4 : 1?

 A

35 mins.

 B

36 mins.

 C

34 mins.

 D

37 mins.

Soln.
Ans: a

Let the time taken by the slower pipe alone be x. Then 7 × $(1/x + 4/x)$ = 1. Solving for x, we get x = 7 × 5 = 35 mins.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 020" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-24.

Posted by Parveen(Hoven),
Aptitude Trainer


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