Pipes and Cisterns Quiz Set 012

Advertisement


Your Score
Correct Answers:
Wrong Answers:
Unattempted:

Question 1

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 2

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 3

A bucket can be filled by a tap in 2 minutes. Another tap on the same bucket can empty it in 12 mins. How long will it take to fill the bucket if both the taps are opened together?

 A

$2{2/5}$ mins.

 B

$4{1/4}$ mins.

 C

1 mins.

 D

$3{6/7}$ mins.

Soln.
Ans: a

Net part filling in one hour is $1/x - 1/y$ = $(y - x)/(xy)$. So complete filling occurs in $(xy)/(y - x)$ = ${2 × 12}/{12 - 2}$ = ${12/5}$, which is same as: $2{2/5}$ mins.


Question 4

Two pipes, A and B, can fill a bucket in 17 and 9 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 7 mins if B is turned off after how many minutes:

 A

$5{5/17}$ mins.

 B

$6{11/16}$ mins.

 C

$3{16/19}$ mins.

 D

$7{8/19}$ 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 $7/17$ + $x/9$ = 1. Solving, we get x = ${90/17}$, which is same as: $5{5/17}$.


Question 5

Tap X can fill the tank in 18 mins. Tap Y can empty it in 9 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is $5/17$th full of water?

 A

$5{5/17}$ mins.

 B

$6{11/16}$ mins.

 C

$3{16/19}$ mins.

 D

$7{8/19}$ mins.

Soln.
Ans: a

1 filled tank can be emptied in ${18 × 9}/{18 - 9}$ mins. So 5/17 can be emptied in ${18 × 9}/{18 - 9}$ × $5/17$ = ${90/17}$, which is same as: $5{5/17}$ mins.


buy aptitude video tutorials


Creative Commons License
This Blog Post/Article "Pipes and Cisterns Quiz Set 012" 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


Advertisement