Pipes and Cisterns Quiz Set 018 | Maths Aptitude Quiz Questions and Mock Test on Pipes and Cisterns Set 18 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

Tap M can fill a cistern in 17 mins. And, a tap N can empty it in 15 mins. In how many minutes will the cistern be emptied if both the taps are opened together when the tank is $11/14$^th already empty?

$27{9/28}$ mins.

$29{10/27}$ mins.

$24{17/30}$ mins.

$28{3/10}$ mins.

Soln.
Ans: a

1 filled cistern can be emptied in ${17 × 15}/{17 - 15}$ mins. So $1 - 11/14$ = $3/14$ filled cistern can be emptied in ${17 × 15}/{17 - 15}$ × $3/14$ = ${765/28}$, which is same as: $27{9/28}$ mins.

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Question 2

A tank is (5/9)^th filled with water. When 9 liters of water are added, it becomes (2/3)^th filled. What is the capacity of the tank?

81 liters.

91 liters.

101 liters.

111 liters.

Soln.
Ans: a

Let x be the capacity in liters. ${5x}/9 + 9 = {2x}/3$. Solving, x = 81 liters.

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Question 3

One tap can fill a tank 4 times faster than the other. If they together fill it in 7 minutes, how much time does the slower alone take to fill the tank?

35 mins.

5 mins.

3 mins.

7 mins.

Soln.
Ans: a

Let the one minute work of the taps be 1/x and 4/x. We have $1/x + 4/x = 1/7$, which gives x = 5 × 7 = 35 mins.

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Question 4

A tank is filled in 16 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 - 48a² - ad² + 16d² = 0.

a³ - 32a² + ad² + 16d² = 0.

a³ - 16a² - ad² + 16d² = 0.

a³ - 80a² + ad² + 16d² = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 16 minutes work of all the taps should add to 1. So we have, $16 × 1/{a - d} + 16 × 1/a + 16 × 1/{a + d}$ = 1, which is same as a³ - 48a² - ad² + 16d² = 0.

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Question 5

Tap X can fill the tank in 19 mins. Tap Y can empty it in 6 mins. In how many minutes will the tank be emptied if both the taps are opened together when the tank is $13/17$^th full of water?

$6{12/17}$ mins.

$8{3/16}$ mins.

$5{2/19}$ mins.

$8{13/19}$ mins.

Soln.
Ans: a

1 filled tank can be emptied in ${19 × 6}/{19 - 6}$ mins. So 13/17 can be emptied in ${19 × 6}/{19 - 6}$ × $13/17$ = ${114/17}$, which is same as: $6{12/17}$ mins.

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