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

21)

If pipe A fills a tank in x hours and another pipe B empties the tank in y hours (where y>x), then which of the following formula gives the time taken to fill the tank when both the pipes?

A)
$\frac{xy}{y - x}$
B)
$\frac{xy}{x - y}$
C)
$\frac{xy}{x + y}$
D)
$\frac{x + y}{x - y}$

Answer: Option A

Explanation

If pipe A fills a tank in x hours and another pipe B empties the tank in y hours (where y>x), then the time taken to fill the tank when both the pipes are open is $\frac{xy}{y - x}$ hours.

Hence option A is correct.

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Discussion

22)

A tap can empty a tank in 60 minutes. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?

A)
20 Minutes
B)
30 Minutes
C)
40 Minutes
D)
10 Minutes

Answer: Option A

Explanation

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

So, $\frac{60 \times 30}{60 + 30} = \frac{1800}{90} = 20 minutes$

The tank will be empties by both the pipe when opened simultaneously in 20 minutes

Hence option A is correct

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Pipes and cisterns

Discussion

23)

Two pipes can fill a tank separately in 120 Minutes and 130 Minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in

A)
62.7 Minutes
B)
62 Minutes
C)
62.4 Minutes
D)
70 Minutes

Answer: Option C

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, $\frac{120 \times 130}{120 + 130} = \frac{15600}{250} = 62.4 minutes$

The tank will be filled by both the pipe when opened simultaneously in 62.4 minutes

Hence option C is correct

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Pipes and cisterns

Discussion

24)

A tap can empty a tank in 60 minutes. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?

A)
20 Minutes
B)
30 Minutes
C)
40 Minutes
D)
10 Minutes

Answer: Option A

Explanation

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

So, $\frac{60 \times 30}{60 + 30} = \frac{1800}{90} = 20 minutes$

The tank will be empties by both the pipe when opened simultaneously in 20 minutes

Hence option A is correct

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Pipes and cisterns

Discussion

25)

Two pipes A and B can fill a tank separately in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

A)
60 hours
B)
30 hours
C)
20 hours
D)
10 hours

Answer: Option C

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, $\frac{36 \times 45}{36 + 45} = \frac{1620}{81} = 20 hours$

The tank will be filled by both the pipe opened simultaneously in 20 hours

Hence option C is correct

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Pipes and cisterns

Discussion

Pipes and cisterns-Basic test 1

Answer: Option A

Answer: Option A

Answer: Option C

Answer: Option A

Answer: Option C