Pipes and Cisterns

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in:

A. 4 hours            

B. 7 hours

C. 8 hours           

D. 14 hours


Answer

                  Ans: Option D

       Explanation:

       Work done by the leak in 1 hour =(1/2)-(3/7)=(1/14)            .

       Leak will empty the tank in 14 hrs. 


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

A. 3 min and 30 sec.

B. 4 min and 30 sec.

C. 4 min.

D. 4 min 77 sec.


Answer

                  Ans: Option C

       Explanation:

Let B be closed after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (9 — x) min  = 1

x[(1/12) + (1/16)] + (9 – x)(1/12) = 1 or (7x/48) + (9-x)/12 = 1

or7x + 36 — 4x = 48 or x=4.

So, B must be closed after 4 minutes. 


3. A pipe can fill a tank in an hour. Because of a leak, it took 1 hour and 10 minutes to fill the tank. Find the time taken by the leak to drain all the water in the tank.

A. 10 minutes

B. 7/6 hours

C. 6/7 hours

D. 7 hours


Answer

                  Ans: Option D

       Explanation:

                  Let the leak take x hours to drain the tank.

       1 hr 10 min = 1+(1/6) = 7/6 hrs

       1-(1/x) = 1-[1/(7/6)] = 1-(6/7)

       Part of tank leaked in an hour = 1-(6/7) = 1/7

       The leak takes 7 hours to drain all the water. 


4. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

A. 3917 hours    

B. 11317 hours

C. 2811 hours    

D. None of the above


Answer

                  Ans: Option A

       Explanation:

Pipes A and B can fill a tank in 5 and 6 hours respectively

=>Part filled by pipe A in hour = 1/5 and Part filled by pipe B in hour = 1/6 .

Pipe C can empty it in 12 hours

=> Part emptied by pipe C in 1 hour = 1/12

Net part filled by Pipes A, B and C together in 1 hour = 15+1/6 − 112 = 1760

i.e, the pipe can be filled in 6017 = 3917 hours 


5. One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened? (Railways 1989)

A. 5 hrs

B. 7 hrs

C. 6 his

D. 8 his


Answer

                  Ans: Option C

       Explanation:

                  Net part filled in 1 hour = (1/2) – (1/3) = 1/6

       Cistern will be full in 6 hours. 


6. An outlet pipe can empty (5/7) of the cistern in half an hour. Find the time taken to empty the full cistern.

A. 70 mins

B. 35 mins

C. 21 3/7 mins

D. 42 mins


Answer

                  Ans: Option D

       Explanation:

       No explanation. 


7. 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 and C are open for one hour each alternately, the tank will be full in:

A. 6 hours           

B. 20/3 hours

C. 7 hours           

D. 15/2  hours


Answer

                  Ans: Option C

       Explanation:

 (A + B)'s 1 hour's work =  (1/12)+(1/15)     =9/60=3/20         .

 (A + C)'s hour's work = (1/12)+(1/20)=8/60=2/15.

Part filled in 2 hrs = (3/20)+(2/15) =17/60 .

Part filled in 6 hrs =3 x (17/60) = 17/20      .

Remaining part =1 – (17/20) = (3/20)

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

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


8. An inlet pipe fills a tank at the rate of 5 liters of water a minute. An outlet connected to the tank can empty a full tank in 5 hours. Both the pipes are opened together for 30 minutes and then, the outlet is closed. It took another 36 minutes to fill the tank. Find the capacity of the tank.

A. 480 liters

B. 360 liters

C. 300 liters

D. 240 liters


Answer

                  Ans: Option C

       Explanation:

Let the inlet pipe take x minutes to fill the tank.

Part of the tank filled by the inlet in a minute = (1/x)

Part of the tank emptied by the outlet in a minute = 1/ (5*60) = 1/300

Part of the tank filled in the first 30 minutes = 30*[(1/x)-(1/300)] = (300-x)/10x

Part of the tank filled in the next 36 minutes = 36*(1/x) 1 – [(300-x)/10x] = 36/x

Solving, x = 60 Capacity of the tank = 60*5 = 300 liters 


9. Two pipes can fill a tank in 25 and 30 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. 250 gallons    

B. 450 gallons

C. 120 gallons    

D. 150 gallons


Answer

                  Ans: Option B

       Explanation:

           Part filled by first pipe in 1 minute= 1/25

Part filled by second pipe in 1 minute= 1/30

Let the waste pipe can empty the full tank in x minutes

Then, part emptied by waste pipe in 1 minute= 1/x

All the three pipes can fill the tank in 15 minutes

i.e., part filled by all the three pipes in 1 minute= 1/15

1/25+1/30−1/x=1/15

or, 1/x=1/25+1/30−1/15

or, 1/x=(6+5−10)/150

or, 1/x=1/150

So, x =150

i.e. the waste pipe can empty the full tank in 150 minutes

Given that waste pipe can empty 3 gallons per minute

i.e. in 150 minutes, it can empty 150 × 3 = 450 gallons

Hence, the volume of the tank = 450 gallons 


10. A tank is filled by two taps in half an hour. If the first tap alone takes 2 hours to fill the tank, find the time taken by the second tap alone to fill the tank.

A. 40 minutes

B. 1 hour

C. 75 minutes

D. 90 minutes


Answer

                  Ans: Option A

       Explanation:

       Part of tank filled by the two taps in 1 minute = 1/30

       Parts of tank filled by tap A in 1 minute = 1/120

       (1/A) + (1/B)=(1/30)

       (1/B) = (1/30)-(1/120)

       (1/B) = (1/40)

       B alone takes 40 minutes to fill the tank. 


11. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many liters does the cistern hold?

A. 7580

B. 8290

C. 7960

D. 8640


Answer

                  Ans: Option D

       Explanation:

       Work done by the inlet in 1 hour = (1/8) – (1/12) = 1/24

       Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440

       Volume of 1/1440 part = 6 liters

       Volume of whole = (1440 x 6) liters = 8640 liters. 


12. An empty drum can be filled with 18 buckets of water, if the capacity of each bucket is 16 liters. How many buckets will be needed to fill the drum if the capacity of each bucket is 12 liters?

A. 28

B. 20

C. 15

D. 24


Answer

                  Ans: Option D

       Explanation:

       Capacity of the drum = 18*16 = 288 liters

       No. of buckets needed = 288/12 = 24 


13. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

A. 81 min.           

B. 108 min.

C. 144 min.         

D. 192 min.


Answer

                  Ans: Option C

       Explanation:

       Let the slower pipe alone fill the tank in x minutes.

       Then, faster pipe will fill it in x/3 minutes.

       1/x+3/x =1/36

       4/x=1/36

       x = 144 min. 


14. Two taps A and B can fill a bathtub in 10 minutes and 15 minutes respectively. If A was open for the first two minutes, B for the next two minutes and so on, the bathtub is filled in

A. 6 minutes

B. 12 minutes

C. 12.5 minutes

D. 24 minutes


Answer

                  Ans: Option B

       Explanation:

       Part of the tub filled in the first 2 minutes = 2*(1/10) = 1/5

       Part of the tub filled in the next 2 minutes = 2*(1/15) = 2/15

       Part of the filled in 4 minutes = (1/5) + (2/15) = 1/3

       Time required to fill the tub = 3*4 = 12 minutes 


15. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

A. 15 min            

B. 20 min

C. 27.5 min         

D. 30 min


Answer

                  Ans: Option D

       Explanation:

       Part filled by pipe A in 1 minute = 1/60

       Part filled by pipe B in 1 minute = 1/40

       Part filled by both pipes A and pipe B in 1 minute

                            = 1/60+1/40=(2+3)/120=5/120=1/24

       Suppose the tank is filled in x minutes

   Then, to fill the tanker from empty state, B is used for x/2 minutes and

       A and B is used for the rest x/2 minutes

       (x/2) × (1/40) + (x/2) × (1/24)=1

       x/2[(1/40)+(1/24)]=1

       (x/2) × (8/120)=1

       (x/2) × (1/15)=1x

       1x=15×2=30 minutes 


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