Pipes and cisterns-Hard level test 2 Solved questions with detailed explanations

11)

Taps M, N and O are attached with the tank and velocity of water coming through them are 24 liters per hour, 65 liters per hour and 84 liters per hour. M and N are inlets and O is outlet. If all the taps are opend together then the tank is filled in 20 h. Calculate the capacity of the tank.

A)
72 liters
B)
48 liters
C)
100 liters
D)
70 liters

Answer: Option C

Explanation

Quantity of water filled in 1 hour(M+N-O)

$= 24 + 65 - 84 = 5 liters$

Quantity of water filled in 20 hours,

$= 20 \times 5 = 100 liters$

So the capacity of the tank is 100 liters

Hence option C is correct.

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Discussion

12)

Two taps A and B can fill a tank in 25 min and 20 min respectively. But the taps are not opened properly, so tap A allows only $\frac{5}{6}$ th part of water and tap B allows only $\frac{2}{3}$ ^rd part of water. Now how long will they take to fill the tank?

A)
12 minutes
B)
13 minutes
C)
14 minutes
D)
15 minutes
E)
16 minutes

Answer: Option D

Explanation

Part of the tank filled by A and B in 1 minute is

$= \frac{1}{25} \times \frac{5}{6} + \frac{1}{20} \times \frac{2}{3} = \frac{2}{30} = 15 minutes$

So the time taken to fill the tank is 15 minutes

Hence option D is correct.

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Discussion

13)

Three taps X, Y and Z are attached with the tank and velocity of water coming through them are 50 liters per hour, 75 liters per hour and 100 liters per hour. X and Z are inlets and Y is outlet. If all the taps are opend together then the tank is filled in 5 h. Calculate the capacity of the tank.

A)
672 liters
B)
375 liters
C)
700 liters
D)
370 liters

Answer: Option B

Explanation

Quantity of water filled in 1 hour is (x+z-y),

$= 50 + 100 - 75 = 75 liters$

Quantity of water filled in 5 hours,

$= 5 \times 75 = 375 liters$

So the capacity of the tank is 375 liters

Hence option B is correct.

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Discussion

14)

A cistern can be filled by two pipes in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 min more?

A)
After 10 minutes
B)
After 20 minutes
C)
After 29 minutes
D)
After 8 minutes

Answer: Option D

Explanation

In 1 min both pipes can fill,

$\Rightarrow \frac{1}{20} + \frac{1}{30} = \frac{1}{12}$ ^th part of the cistern---Eq1

Similarly,

In 10 min only second pipe can fill,

$\Rightarrow \frac{1}{30} \times 10 = \frac{1}{3}$ ^rd part of the cistern

Part of cistern filled by both the pipes,

$\Rightarrow 1 - \frac{1}{3} = \frac{2}{3}$

According to eqution 1, $\frac{1}{12}$ ^th part will be filled in 1 min

So, $\frac{2}{3}$ rd part will be filled in...

$\Rightarrow 12 (\frac{2}{3}) = 8 minutes$

Therefore, firstpipe should be turned off after 8 min

Hence option D is correct.

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Discussion

15)

Pipes M and N can fill a tank in 40 hours and 20 hours respectively. A third pipe O empties the tank in 10 hours. Calculate the time in which the tank will be filled if all the pipes are opened together.

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

Answer: Option B

Explanation

According to the formula, If pipe M and N fills a tank in x and y hours respectively, but a third pipe O empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{xyz}{yz + xz - xy}$ hours.

So,

$\frac{40 \times 20 \times 10}{(40 \times 10) + (20 \times 10) - (40 \times 20)} = \frac{8000}{400 + 200 - 800} = \frac{8000}{200} = 40 hours$

Hence, the tank will be filled in 40 hours when all the pipes are opened simultaneously.

Hence option B is correct.

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Discussion

Pipes and cisterns-Hard test 2

Answer: Option C

Answer: Option D

Answer: Option B

Answer: Option D

Answer: Option B