Pipes and Cisterns Quiz Set 008

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Question 1

A tank is filled in $1{2/13}$ 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

4.

 B

5.

 C

3.

 D

6.

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 ${15/13}$ minutes work of all the taps should add to 1. So we have, ${15/13}$ × $(1/{1 - d} + 1/1 + 1/{1 + d})$ = 1, which is same as $2/{1 - d^2} + 1$ = ${13/15}$. Solving we get d = ±4.


Question 2

A tank is filled in 13 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 - 39a2 - ad2 + 13d2 = 0.

 B

a3 - 26a2 + ad2 + 13d2 = 0.

 C

a3 - 13a2 - ad2 + 13d2 = 0.

 D

a3 - 65a2 + ad2 + 13d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 13 minutes work of all the taps should add to 1. So we have, $13 × 1/{a - d} + 13 × 1/a + 13 × 1/{a + d}$ = 1, which is same as a3 - 39a2 - ad2 + 13d2 = 0.


Question 3

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 4

Two pipes, A and B, can fill a bucket in 13 and 14 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 6 mins if B is turned off after how many minutes:

 A

$7{7/13}$ mins.

 B

$9{1/4}$ mins.

 C

$5{2/3}$ mins.

 D

$9{2/15}$ mins.

Soln.
Ans: a

Let B be closed after it has been filling for x minutes. Work done by pipes A and B should add to 1. So $6/13$ + $x/14$ = 1. Solving, we get x = ${98/13}$, which is same as: $7{7/13}$.


Question 5

Two taps X, Y and Z can fill a tank in 4, 18 and 7 minutes respectively. All the taps are turned on at the same time. After how many minutes is the tank completely filled?

 A

$2{26/113}$ mins.

 B

$3{29/112}$ mins.

 C

$1{24/115}$ mins.

 D

$5{16/115}$ mins.

Soln.
Ans: a

Let the time be x mins. Then sum of works done by X, Y and Z = 1. $x/4 + x/18 + x/7 = 1$. Solving, we get x = $2{26/113}$. 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.


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Creative Commons License
This Blog Post/Article "Pipes and Cisterns Quiz Set 008" 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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