Pipes and Cisterns Quiz Set 006

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Question 1

A tank is filled in $1{2/33}$ 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

6.

 B

7.

 C

5.

 D

8.

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 ${35/33}$ minutes work of all the taps should add to 1. So we have, ${35/33}$ × $(1/{1 - d} + 1/1 + 1/{1 + d})$ = 1, which is same as $2/{1 - d^2} + 1$ = ${33/35}$. Solving we get d = ±6.


Question 2

A tank is (2/5)th filled with water. When 44 liters of water are added, it becomes (8/9)th filled. What is the capacity of the tank?

 A

90 liters.

 B

100 liters.

 C

110 liters.

 D

120 liters.

Soln.
Ans: a

Let x be the capacity in liters. ${2x}/5 + 44 = {8x}/9$. Solving, x = 90 liters.


Question 3

One tap can fill a tank 2 times faster than the other. If they together fill it in 9 minutes, how much time does the slower alone take to fill the tank?

 A

27 mins.

 B

3 mins.

 C

4 mins.

 D

5 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 2/x. We have $1/x + 2/x = 1/9$, which gives x = 3 × 9 = 27 mins.


Question 4

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 5

Tap X can fill the tank in 11 mins. Tap Y can empty it in 5 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is $8/10$th full of water?

 A

$7{1/3}$ mins.

 B

$12{1/2}$ mins.

 C

$6{1/3}$ mins.

 D

$6{1/5}$ mins.

Soln.
Ans: a

1 filled tank can be emptied in ${11 × 5}/{11 - 5}$ mins. So 8/10 can be emptied in ${11 × 5}/{11 - 5}$ × $8/10$ = ${22/3}$, which is same as: $7{1/3}$ mins.


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This Blog Post/Article "Pipes and Cisterns Quiz Set 006" 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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