Pipes and cisterns-Basic level test 1 Solved previous year questions with detailed explanations

1)

Pipe A completely fills the tank in 8 hours, then what part of the tank will be filled by pipe A in 1 hour?

A)
$\frac{1}{6}$
B)
$\frac{5}{6}$
C)
$\frac{1}{8}$
D)
$\frac{1}{4}$

Answer: Option C

Explanation

According to the formula, if a pipe can comletely fill a tank in x hours, then the portion filled in 1 hour is $\frac{1}{x}$ .

As Pipe A completely fills the tank in 8 hours.

$\frac{1}{8}$ ^thpart of the tank will be filled by pipe A in 1 hour.

Hence option C is correct

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Discussion

2)

An inlet pipe fills $\frac{1}{14}$ ^th part of the tank in 1 hour. How much time will the inlet pipe take to fill the tank?

A)
14
B)
2
C)
4
D)
10

Answer: Option A

Explanation

According to the formula, If pipe A fills $\frac{1}{x}$ portion of the tank in 1 hour, then the time taken by the pipe to fill the full tank is x hours.

As inlet pipe fills $\frac{1}{14}$ ^th part of the tank in 1 hour. It will take 14 hours to fill the tank.

Hence option A is correct

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Discussion

3)

A tank can be filled up in 4 hours by an inlet A. And an outlet B can empty the tank in 8 hours. If both inlet and outlet are opened simultaneously, then after how much time will the tank get filled?

[Bank Clerks 2009]

A)
14 hours
B)
2 hours
C)
4 hours
D)
8 hours

Answer: Option D

Explanation

According to the formula, if pipe A can comletely fill a tank in x hours and pipe B can empty the same tank in y hours, then the time taken to fill the tank when both the pipes are opened simultaneously is $\frac{xy}{x - y}$ hours.

so, $\frac{4 \times 8}{8 - 4} = \frac{32}{4} = 8 hours$

The tank will be filled in 8 hours when both the pipes are opened simultaneously.

Hence option D is correct

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Discussion

4)

A pipe can fill the tank in 10 hours. While another pipe can empty the tank in 6 hours. Find the time taken to empty the tank when both the pipes are opened together.

[Bank Clerks 2010]

A)
15 hours
B)
12 hours
C)
14 hours
D)
18 hours

Answer: Option A

Explanation

According to the formula, if pipe A can comletely fill a tank in x hours and pipe B can empty the same tank in y hours, then the time taken to fill the tank when both the pipes are opened simultaneously is $\frac{xy}{x - y}$ hours.

so, $\frac{10 \times 6}{10 - 6} = \frac{60}{4} = 15 hours$

The tank will be emptied in 15 hours when both the pipes are opened simultaneously.

Hence option A is correct

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Discussion

5)

Pipe A can fill the tank in 30 hours, while pipe B can fill the same tank in 10 hours, Pipe C can empty this full tank in 40 hours. If all the three pipes are opened simultaneously, how much time is needed to completely fill the tank?

[Hotel mgmt. 2010]

A)
$9 \frac{3}{13} hours$
B)
$9 \frac{4}{13} hours$
C)
$9 \frac{7}{13} hours$
D)
$9 \frac{9}{13} hours$

Answer: Option A

Explanation

According to the formula, If pipe A and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then full tank will be filled in $\frac{xyz}{yz + xz - xy}$ hours.

So,

$\frac{30 \times 10 \times 40}{(30 \times 40) + (10 \times 40) - (30 \times 10)} = \frac{12000}{400 + 1200 - 300} = \frac{12000}{1300} = 9 \frac{3}{13} hours$

The tank will be filled in $9 \frac{3}{13}$ hours when all the pipes are opened simultaneously.

Hence option A is correct

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Discussion

Pipes and cisterns-Basic test 1

Answer: Option C

Answer: Option A

Answer: Option D

Answer: Option A

Answer: Option A