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**Quiz Description** :

**Name: **Pipe and Cistern Test – 2

**Subject: **Aptitude

**Topic: **Pipe and Cistern

**Questions: **12 Objective type

**Time Allowed: **20 minutes

**Important for: **SSC, IBPS, UPSSC, UPSC, UPPSC, Job Interview exams.

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- Review

- Question 1 of 12
##### 1. Question

1 pointsIf three taps are opened together, a tank is filled in 12 hours. One of the taps can fill it in 10 hours and another in 15 hours. How does the third tap work?

CorrectWe have to find the nature of the third tap i.e. whether this pipe is a filler or a waste pipe.

Let it be a filler pipe which fills in x hours.

Then, (10 × 15 × x)/(10 ×15 + 10x +15x )=12

150x = 150 × 12 + 25x × 12

-150x = 1800

∴ x = -12

-ve sign shows that the third pipe is a waste pipe which vacates the tank in 12 hours.IncorrectWe have to find the nature of the third tap i.e. whether this pipe is a filler or a waste pipe.

Let it be a filler pipe which fills in x hours.

Then, (10 × 15 × x)/(10 ×15 + 10x +15x )=12

150x = 150 × 12 + 25x × 12

-150x = 1800

∴ x = -12

-ve sign shows that the third pipe is a waste pipe which vacates the tank in 12 hours. - Question 2 of 12
##### 2. Question

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

CorrectTime taken = (36 × 45)/(36 + 45) = 20 hrs

IncorrectTime taken = (36 × 45)/(36 + 45) = 20 hrs

- Question 3 of 12
##### 3. Question

1 pointsA tank is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the cistern is full, in how many hours will the leak empty the tank?

CorrectIt is clear from the given question that the filler pipe fills the tank in 8 hours and if both the filler and the leak work together, the tank is filled in 8 hours. Therefore, the leak will empty the tank in (10 × 8)/(10 – 8) = 40 hours.

IncorrectIt is clear from the given question that the filler pipe fills the tank in 8 hours and if both the filler and the leak work together, the tank is filled in 8 hours. Therefore, the leak will empty the tank in (10 × 8)/(10 – 8) = 40 hours.

- Question 4 of 12
##### 4. Question

1 pointsA pipe can fill a tank in 15 hours. Due to a leak in the bottom, it is filled in 20 hours. If the tank is full, how much time will the leak take to empty it?

CorrectIncorrect - Question 5 of 12
##### 5. Question

1 pointsA tank is normally filled in 12 hours but takes 2 hours longer to fill because of a leak in its bottom. If the cistern is full, in how many hours will the leak empty the tank?

CorrectIt is clear from the given question that the filler pipe fills the tank in 8 hours and if both the filler and the leak work together, the tank is filled in 8 hours. Therefore, the leak will empty the tank in (14 × 12)/(14 – 12) = 84 hours.

IncorrectIt is clear from the given question that the filler pipe fills the tank in 8 hours and if both the filler and the leak work together, the tank is filled in 8 hours. Therefore, the leak will empty the tank in (14 × 12)/(14 – 12) = 84 hours.

- Question 6 of 12
##### 6. Question

1 pointsPipe A can fill a tank in 20 hours while pipe B alone can fill it in 30 hours and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will be needed to make the tank full?

CorrectRequired time= (20 × 30 × 45)/(30 × 40 + 20 × 40 – 20 × 30) = 120/7 hrs.

IncorrectRequired time= (20 × 30 × 45)/(30 × 40 + 20 × 40 – 20 × 30) = 120/7 hrs.

- Question 7 of 12
##### 7. Question

1 pointsA pipe can fill a tank in 24 hours. Due to a leak in the bottom, it is filled in 32 hours. If the tank is full, how much time will the leak take to empty it?

CorrectRequired time= (32 × 24)/(32- 24) = 96 hrs

IncorrectRequired time= (32 × 24)/(32- 24) = 96 hrs

- Question 8 of 12
##### 8. Question

1 pointsTwo pipes P and Q would fill a cistern in 24 hours and 32 hours respectively. If both are opened together, find when the first pipe must be turned off so that the cistern may be just filled in 16 hours.

CorrectThe first pipe should work for = (1- 16/32)×24 hours = 12 hours

IncorrectThe first pipe should work for = (1- 16/32)×24 hours = 12 hours

- Question 9 of 12
##### 9. Question

1 pointsA pipe can fill a tank in 12 minutes and another pipe in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then the third pipe is also opened. In what time is the cistern emptied?

CorrectCistern filled in 5 minutes = 5 (1/12+1/15)= 3/4

Net work done by 3 pipes in 1 minute = (1/12+1/15)- 1/6= -1/60

-ve sign shows that 1/60 part is emptied in 1 minutes.

∴ 3/4 part is emptied in 60 × 3/4=45 minutes.IncorrectCistern filled in 5 minutes = 5 (1/12+1/15)= 3/4

Net work done by 3 pipes in 1 minute = (1/12+1/15)- 1/6= -1/60

-ve sign shows that 1/60 part is emptied in 1 minutes.

∴ 3/4 part is emptied in 60 × 3/4=45 minutes. - Question 10 of 12
##### 10. Question

1 pointsA tank has a leak which would empty it in 8 hrs. A tap is turned on which admits 6 liters a minutes into the tank, and it is now emptied in 12 hrs. How many liters does the tank hold?

CorrectThe filler tap can fill the tank in = (12 × 8)/(12 – 8) = 24 hrs.

∴ Capacity of tank = 24 × 60 × 6 = 8640 liters.IncorrectThe filler tap can fill the tank in = (12 × 8)/(12 – 8) = 24 hrs.

∴ Capacity of tank = 24 × 60 × 6 = 8640 liters. - Question 11 of 12
##### 11. Question

1 pointsA cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leaks will empted the tank in how much time?

CorrectThe leak will empty in = (8 × (8 + 2))/2 = 40 hours

IncorrectThe leak will empty in = (8 × (8 + 2))/2 = 40 hours

- Question 12 of 12
##### 12. Question

1 pointsIf two pipes function simultaneously, the reservoir is filled in 12 hrs. On pipe fills the reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

CorrectLet the faster pipe fills the tank in x hours.

Then the slower pipe fills the tank in ‘x + 10’ hours.

When both of them are opened, the reservoir will be filled in = (x (x + 10 ))/(x + (x + 10)) = 12

x2 – 14x – 120 = 0

∴ x = 20, -6

But x can’t be –ve, hence the faster pipe will fill the reservoir in 20 hours.IncorrectLet the faster pipe fills the tank in x hours.

Then the slower pipe fills the tank in ‘x + 10’ hours.

When both of them are opened, the reservoir will be filled in = (x (x + 10 ))/(x + (x + 10)) = 12

x2 – 14x – 120 = 0

∴ x = 20, -6

But x can’t be –ve, hence the faster pipe will fill the reservoir in 20 hours.