Pipes and Cistern Questions

FACTS  AND  FORMULAE  FOR  PIPES  AND  CISTERN  QUESTIONS

 

 

1. Inlet : A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

 

2. Outlet : A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

 

(i) If a pipe can fill a tank in x hours, then:

part filled in 1 hour = 1/x

(ii) If a pipe can empty a tank in y hours, then:

part emptied in 1 hour = 1/y

(iii) If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = 1x-1y

(iv) If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes,  the net part emptied in 1 hour = 1y-1x

Q:

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

A) 10 min. 20 sec. B) 11 min. 45 sec.
C) 12 min. 30 sec. D) 14 min. 40 sec.
 
Answer & Explanation Answer: D) 14 min. 40 sec.

Explanation:

Part filled in 4 minutes =4(1/15+1/20) = 7/15

 

Remaining part =(1-7/15) = 8/15

 

Part filled by B in 1 minute =1/20 : 8/15 :: 1:x 

x = (8/15*1*20) = 1023min = 10min 40sec

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

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48 34121
Q:

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A) 10 B) 12
C) 14 D) 16
 
Answer & Explanation Answer: C) 14

Explanation:

Part filled in 2 hours = 2/6=1/3

 

Remaining part =1-13=23

 

 (A + B)'s 7 hour's work = 2/3

 

(A + B)'s 1 hour's work = 2/21

 

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

 

=1/6-2/21 = 1/14

 

C alone can fill the tank in 14 hours.

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31 13434
Q:

A pump can fill a tank with water in 2 hours. Because of a leak, it took 213 hours to fill the tank. The leak can drain all the water of the tank in:

A) 7 hours B) 8 hours
C) 12 hours D) 14 hours
 
Answer & Explanation Answer: D) 14 hours

Explanation:

If the total area of pump=1 part

The pumop take 2 hrs to fill 1 part 

The pumop take1 hour to fill 1/2 portion 

 

Due to lickage  

The pumop take 7/3 hrs to fill 1 part 

The pumop take1 hour to fill 3/7 portion 

Now the difference of area = (1/2-3/7)=1/14 

 

This 1/14 part of water drains in 1 hour 

Total area=1 part of water drains in (1x14/1)hours= 14 hours 

 

So the leak can drain all the water of the tank in 14 hours. 

Leak will empty the tank in 14 hrs

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27 12561
Q:

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A) 3 hrs 15 min B) 3 hrs 45 min
C) 4 hrs 15 min D) 4 hrs 1
 
Answer & Explanation Answer: B) 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

 

  Part filled by the four taps in 1 hour =4*1/6 =2/3

 

Remaining part =1-12=12

 

23:12::1:x

 

=> x = 12*1*32=34

 

So, total time taken = 3 hrs. 45 mins.

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15 10582
Q:

Three taps A,B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B ,C are open for one hour each alternatively, the tank will be full in:

A) 6 hrs B) 20/3 hrs
C) 7 hrs D) 15/2 hrs
 
Answer & Explanation Answer: C) 7 hrs

Explanation:

A+B's 1 hour work=112+115=960=320

A+C's 1 hour work=112+120=860=215  

 

part filled in 2 hrs=320+215=1760  

 

part filled in 6 hrs=3*1760=1720  

 

 remaining part =1-1720=320  

 

Now, it is  the turn of A and B (3/20) part is filled by A and B in 1 hour.

Therefore, Total  time taken to fill the tank =(6+1)hrs= 7 hrs

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21 10550
Q:

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

A) 60 gallons B) 100 gallons
C) 120 gallons D) 180 gallons
 
Answer & Explanation Answer: C) 120 gallons

Explanation:

Work done by the waste pipe in 1 minute =115-120+124=115-11120 = -140 [-ve sign means emptying]

 

Volume of 140part = 3 gallons

 

Volume of whole = (3 x 40) gallons = 120 gallons.

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15 10445
Q:

A 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 leak will empty it in    ?

A) 20 hrs B) 28 hrs
C) 36 hrs D) 40 hrs
 
Answer & Explanation Answer: A) 20 hrs

Explanation:

1/8 - 1/x = 1/10

 => x = 40 hrs

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26 9032
Q:

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400  m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A) 50 m^3/min B) 60 m^3/min
C) 72 m^3/min D) None of these
 
Answer & Explanation Answer: A) 50 m^3/min

Explanation:

Let the filling capacity of the pump be x m3/min. 

Then, emptying capacity of the pump=(x+10)m3/min.  

so,2400x-2400x+10=8 x2+10x-3000=0 

 

x-50+x+60=0 x=50

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20 8876