Pipes and cisterns-Basic level test 2 Solved previous year questions with detailed explanations

1)

Two pipes A and B can fill a tank separately in 10 min and 20 min respectively. If both the pipes are used together, how much time will be taken to fill the tank?

A)
$6 \frac{1}{2} \min$
B)
$6 \frac{3}{2} \min$
C)
$6 \frac{5}{7} \min$
D)
$6 \frac{2}{3} \min$

Answer: Option D

Explanation

According to the formula, if pipe A can comletely fils a tank in x hours and pipe B can comletely fill a tank in y hours, then the time taken by both pipes together to fill the tank is $\frac{xy}{x + y}$ hours.

So, $\frac{10 \times 20}{10 + 20} = \frac{200}{30} = 6 \frac{2}{3} minutes$

The tank will be filled by both the pipe opened simultaneously in $6 \frac{2}{3}$ hours

Hence option D is correct

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Discussion

2)

A cistern can be filledup in 14 hours by an inlet M. Another outlet N can empty the cistern in 18 hours. If both the inlets M and N are opened together, then after how long will the cistern be fully filled?

A)
53 hours
B)
63 hours
C)
45 hours
D)
29 hours

Answer: Option B

Explanation

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

So, $\frac{14 \times 18}{18 - 14} = \frac{252}{4} = 63 hours$

The tank will be filled by both the pipe opened simultaneously in 63 hours

Hence option B is correct

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Pipes and cisterns

Discussion

3)

A pipe can fill a tank in 20 hours. Due to a leak in the bottom, it is filled in 40 hours. If the tank is full, how much time will the leak take to empty it?

A)
40 hours
B)
30 hours
C)
50 hours
D)
20 hours

Answer: Option A

Explanation

According to the above given formula, if pipe A can completely fils a tank in x hours and pipe B can comletely empty the tank in y hours, then the time taken by both pipes together to fill the tank is $\frac{xy}{x - y}$ hours.

So, $\frac{20 \times 40}{40 - 20} = \frac{800}{20} = 40 hours$

The tank will be filled by both the pipe opened simultaneously in 40 hours

Hence option A is correct

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Pipes and cisterns

Discussion

4)

Two pipes A and B can fill a tank in 12 and 16 min respectively. If both the pipes are opened together, then calculate the time after which B should be closed, so that the tank is full in 9 minutes.

A)
4 minutes
B)
6 minutes
C)
2 minutes
D)
8 minutes

Answer: Option A

Explanation

According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is $\{y [1 - \frac{t}{x}]\}$ min.

So, $\{16 [1 - \frac{9}{12}]\} = 16 \times \frac{3}{12} = 4 \min$

The tank will be filled in 4 min both the pipes are opened simultaneously.

Hence option A is correct

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Pipes and cisterns

Discussion

5)

If two pipes A and B can fill a tank in t min. If time taken by A alone is 4 minutes more than t and time taken by B alone is 25 minutes more than t, then the time taken by both the pipes together is?

A)
34 minutes
B)
16 minutes
C)
10 minutes
D)
48 minutes

Answer: Option C

Explanation

According to the above given formula, Two pipes A and B can together fill a tank in time T. If time taken by pipe A alone is more than T by x and the time taken by pipe B alone is more than T by y, then T is $\sqrt{xy}$ min.

So, $T = \sqrt{4 \times 25} = \sqrt{100} = 10 \min$

The tank will be completely filled in 10 min.

Hence option C is correct

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Pipes and cisterns

Discussion

Pipes and cisterns-Basic test 2

Answer: Option D

Answer: Option B

Answer: Option A

Answer: Option A

Answer: Option C