Pipes and Cisterns Quiz Set 003

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Question 1

Two taps A and B can fill a tank in 16 and 32 minutes respectively. Both the taps are turned on at the same time. After how many minutes should B be turned off so that the tank can be filled in 12 minutes?

 A

8 mins.

 B

9 mins.

 C

7 mins.

 D

11 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. $12/16 + x/32 = 1$. Solving, we get x = 8.


Question 2

A tank is filled in 11 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 - 33a2 - ad2 + 11d2 = 0.

 B

a3 - 22a2 + ad2 + 11d2 = 0.

 C

a3 - 11a2 - ad2 + 11d2 = 0.

 D

a3 - 55a2 + ad2 + 11d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 11 minutes work of all the taps should add to 1. So we have, $11 × 1/{a - d} + 11 × 1/a + 11 × 1/{a + d}$ = 1, which is same as a3 - 33a2 - ad2 + 11d2 = 0.


Question 3

A tap can fill a tank in 2 hours. Because of a leak it took $2{3/8}$ hours to fill the tank. When the tank has been completely filled, the tap is closed. How long will the water last in the tank?

 A

$12{2/3}$ hrs.

 B

$20{1/2}$ hrs.

 C

$11{2/3}$ hrs.

 D

$9{2/5}$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is $1/2 - 1/({19/8})$ = $1/2 - 8/19$ = $3/38$. So the leak will complete the whole task in ${38/3}$, which is same as: $12{2/3}$ hours.


Question 4

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 5

A tank is filled in 17 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 - 51a2 - ad2 + 17d2 = 0.

 B

a3 - 34a2 + ad2 + 17d2 = 0.

 C

a3 - 17a2 - ad2 + 17d2 = 0.

 D

a3 - 85a2 + ad2 + 17d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 17 minutes work of all the taps should add to 1. So we have, $17 × 1/{a - d} + 17 × 1/a + 17 × 1/{a + d}$ = 1, which is same as a3 - 51a2 - ad2 + 17d2 = 0.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 003" 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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