Pipes and Cisterns Quiz Set 017 | Maths Aptitude Quiz Questions and Mock Test on Pipes and Cisterns Set 17 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

Two pipes, A and B, can fill a bucket in 15 and 19 mins respectively. Both the pipes are opened simultaneously. The bucket is filled in 5 mins if B is turned off after how many minutes:

$12{2/3}$ mins.

$20{1/2}$ mins.

$11{2/3}$ mins.

$9{2/5}$ 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 $5/15$ + $x/19$ = 1. Solving, we get x = ${38/3}$, which is same as: $12{2/3}$.

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Question 2

A tap can fill a tank in 2 hours. Because of a leak it took $2{2/7}$ 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?

16 hrs.

17 hrs.

15 hrs.

$6{1/3}$ hrs.

Soln.
Ans: a

Work done by the leak in one hour is $1/2 - 1/({16/7})$ = $1/2 - 7/16$ = $2/32$. So the leak will complete the whole task in 16 hours.

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Question 3

Two taps A and B can fill a tank in 15 and 30 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 13 minutes?

30 mins.

5 mins.

3 mins.

7 mins.

Soln.
Ans: a

Let B be closed after x mins. Then sum of works done by A and B = 1. $13/15 + x/30 = 1$. Solving, we get x = 4.

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Question 4

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?

a³ - 51a² - ad² + 17d² = 0.

a³ - 34a² + ad² + 17d² = 0.

a³ - 17a² - ad² + 17d² = 0.

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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