Pipes and Cisterns Quiz Set 014

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Question 1

A tank is filled in $1{1/3}$ minutes by three taps running together. Times taken by the three taps to independently fill the tank are in an AP[Arithmetic Progression]. If the first tap is a leakage tap and the second tap takes 1 minute to fill the tank, then, the common difference of the AP can be?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

Let the times taken by the three taps be 1 - d, 1 and 1 + d. The time taken by the first tap will be negative because it is a leakage tap. Then ${4/3}$ minutes work of all the taps should add to 1. So we have, ${4/3}$ × $(1/{1 - d} + 1/1 + 1/{1 + d})$ = 1, which is same as $2/{1 - d^2} + 1$ = ${3/4}$. Solving we get d = ±3.


Question 2

A city tanker is filled by two large pipes, X and Y, together in 42 and 28 minutes respectively. On a certain day, pipe Y is used for first half of the time, and both X and Y are used for the second half. How many minutes does it take to fill the tank?

 A

21 mins.

 B

22 mins.

 C

20 mins.

 D

23 mins.

Soln.
Ans: a

Let the time taken be x. Y is running for x mins, and X for x/2. So $(x/28 + x/{2 × 42})$ = 1. Solving for x, we get x = 21 mins.


Question 3

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 4

A bucket can be filled by a tap in 5 minutes. Another tap on the same bucket can empty it in 10 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 $(xy)/(y - x)$ = ${5 × 10}/{10 - 5}$ = 10 mins.


Question 5

What is the volume of the tank in liters if it measures 9m × 6m × 9m?

 A

486000 liters.

 B

486 liters.

 C

3240 liters.

 D

72900 liters.

Soln.
Ans: a

The volume in m3 is 9 × 6 × 9 = 486m3. But 1m3 = 1000L. So volume in liters = 486 × 1000 = 486000L.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 014" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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