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# Maths : Pipes & Cisterns (Solved in Steps)

1. 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

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
==> 1/x=1/25+1/30″1/15 = (6+5-10)/150=1/150
==> 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 ie, in 150 minutes, it can empty 150 x 3 = 450 gallons Hence, the volume of the tank = 450 gallons

2. A tank is filled in 10 hours by three pipes A, B and C.
The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

A. 70 hours B. 30 hours
C. 35 hours D. 50 hours

Explanation:

Let the pipe A can fill the tank in x hours
Then pipe B can fill the tank in x/2 hours and pipe C can fill the tank in x/4 hours
Part filled by pipe A in 1 hour = 1/x
Part filled by pipe B in 1 hour = 2/x
Part filled by pipe C in 1 hour = 4/x
Part filled by pipe A, pipe B and pipe C in 1 hour = 1/x+2/x+4/x=7/x
i.e., pipe A, pipe B and pipe C can fill the tank in x/7 hours
Given that pipe A, pipe B and pipe C can fill the tank in 10 hours
=>x/7=10
==>x=10×7=70 hours

3. One pipe can fill a tank four 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. 180 min B. 144 min
C. 126 min D. 114 min

Explanation:

Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes
Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 4/x
Part filled by both the pipes in 1 minute = 1/x+4/x
It is given that both the pipes together can fill the tank in 36 minutes
Part filled by both the pipes in 1 minute = 1/36
1/x+4/x=1/36
5/x=1/36
x=5×36=180
ie., the slower pipe alone fill the tank in 180 minutes

4. A tap can fill a tank in 4 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 hr B. 1 hr 30 min
C. 2 hr 30 min D. 2 hr

Explanation:

A tap can fill a tank in 4 hours
= > The tap can fill half the tank in 2 hours
Remaining part = 1/2
After half the tank is filled, three more similar taps are opened.
Hence, total number of taps becomes 4.
Part filled by one tap in 1 hour = ¼
Part filled by four taps in 1 hour = 4×1/4=1
i.e., 4 taps can fill remaining half in 30 minutes Total time taken = 2 hour + 30 minute = 2 hour 30 minutes

5. A tap can fill a tank in 4 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

A. 1 hr 20 min B. 4 hr
C. 3 hr D. 2 hr 40 min

Explanation:

A tap can fill a tank in 4 hours
=> The tap can fill half the tank in 2 hours
Remaining part = 1/2
After half the tank is filled, two more similar taps are opened.
Hence, total number of pipes becomes 3.
Part filled by one tap in 1 hour = ¼
Part filled by three taps in 1 hour = 3×1/4=3/4
Time taken to fill12the tank by 3 pipes = (1/2) + (3/4) =4/6
==2/3 hour = 40 minutes
Total time taken = 2 hour + 40 minute = 2 hour 40 minutes

6. 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

Explanation :

A, B and C can fill a tank in 6 hours.
==>Part filled by pipes A,B and C in 1 hr = 1/6
All these pipes are open for only 2 hours and then C is closed.
Part filled by pipes A,B and C in these 2 hours = 2/6=1/3
Remaining part = 1-(1/3) =2/3
This remaining part of 2/3 is filled by pipes A and B in 7 hours
===>Part filled by pipes A and B in 1 hr ={(2/3) + 7} =2/21
Part filled by pipe C in 1 hr = (1/6-2/21)=(7-4)/42=3/42=1/14 i.e., C alone can fill the tank in 14 hours

7. 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

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=1
x=15×2=30 minutes

8. 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. 623 hours B. 6 hours
C. 712 hours D. 7 hours

Explanation :

Part filled by pipe A in 1 hour = 1/12
Part filled by pipe B in 1 hour = 1/15
Part filled by pipe C in 1 hour = 1/20
In the first hour, A and B is open In the second hour, A and C is open then this pattern goes on till the tank fills
Part filled by pipe A and pipe B in 1 hour
= 1/12+1/15=9/60=3/20
Part filled by pipe A and pipe C in 1 hour
= 1/12+1/20=8/60=2/15
Part filled in 2 hour = 3/20+2/15=17/60
Part filled in 6 hour = (17/60) x3=17/20
Remaining part = (1-(17/20) =3/20
Now, 6 hours are over and only 3/20 part needed to be filled. At this 7th hour, A and B is openTime taken by pipe A and B to fill this 3/20 part
= (3/20) + (3/20)
= 1 hour
Total time taken = 6 hour + 1 hour = 7 hour

9. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many litres does the cistern hold?

A. 4010 litre B. 2220 litre C. 1920 litre D. 2020 litre

Explanation :

Part emptied by the leak in 1 hour = 1/6
Net part emptied by the leak and the inlet pipe in 1 hour = 1/24
Part filled by the inlet pipe in 1 hour = 1/6″1/24=1/8
i.e., inlet pipe fills the tank in 8 hours = (8 x 60) minutes = 480 minutes
Given that the inlet pipe fills water at the rate of 4 litres a minute
Hence, water filled in 480 minutes = 480 x 4 = 1920 litre
i.e., The cistern can hold 1920 litre

10. A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

A. 4.8 hr B. 2.4 hr
C. 3.6 hr D. 1.8 hr

Explanation:

Part filled by the first tap in 1 hour = 1/3
Part emptied by the second tap 1 hour = 1/8
Net part filled by both these taps in 1 hour = 1/3-1/8=5/24
i.e, the cistern gets filled in 24/5 hours = 4.8 hours

11. Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 40 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?

A. 28 hr B. 16 hr
C. 22 hr D. 32 hr

Explanation :

Part filled by pipe A in 1 hour = 1/5
Part filled by pipe B in 1 hour = 1/20
Part filled by pipe A and B in 1 hour = 1/5+1/20=1/4
i.e., A and B together can fill the tank in 4 hours
Given that due to the leakage, it took 40 minutes more to fill the tank.
i.e., due to the leakage, the tank got filled in 4(40/
60) hour =4(2/3) hour=14/3 hour
==> Net part filled by pipe A and B and the leak in 1 hour = 3/14
==>Part emptied by the leak in 1 hour =1/4″3/14=1/28
i.e., the leak can empty the tank in 28 hours

12. Bucket P has thrice the capacity as bucket Q. It takes 80 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?

A. 30 B. 45
C. 60 D. 80

Explanation :

Let capacity of bucket P = x
Then capacity of bucket Q = x/3
Given that it takes 80 turns for bucket P to fill the empty drum
=> capacity of the drum = 80x
Number of turns required if both P and Q are used
= 80x+(x+(x/3))
=240x+(3x+x)
=240+4
=60

13. Two pipes A and B can separately fill a cistern in 40 minutes and 30 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 20 minutes. In how much time, the third pipe alone can empty the cistern?

A. 120 min B. 100 min
C. 140 min D. 80 min

Explanation :

Part filled by pipe A in 1 minute = 1/40 Part filled by pipe B in 1 minute = 1/30
Net part filled by pipe A, pipe B and the third pipe in 1 hour = 1/20
===>Part emptied by the third pipe in 1 hour = (1/40)+(1/30)”(1/20) =(3+4″6)/120=1/120
i.e., third pipe alone can empty the cistern in 120 minutes

14. Two pipes A and B can fill a tank in 9 hours and 3 hours respectively. If they are opened on alternate hours and if pipe A is opened first, how many hours, the tank shall be full?

A. 4 hr B. 5 hr
C. 2 hr D. 6 hr

Explanation :

Part filled by pipe A in 1hour =1/9
Part filled by pipe B in 1hour =1/3
Pipe A and B are opened alternately.
Part filled in every 2 hour = 1/9+1/3=(1+3)/9 =4/9
Part filled in 4 hour = 2x(4/9)=8/9 remaining part =1-(8/9)
=1/9
Now it is pipe A’s turn.
Time taken by pipe A to fill the remaining 19 part =(1/9)+ (1/9)=1 hour
Total time taken = 4 hour + 1hour = 5 hour

15. 13 buckets of water fill a tank when the capacity of each bucket is 51 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 17 litres?

A. 33 B. 29
C. 39 D. 42

Explanation:

Capacity of the tank = (13 x 51) litre
Number of buckets required of capacity of each bucket is 17 litre = (13×51)/17
=13×3=39

16. Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?

A. 2.4 hr B. 3 hr
C. 4 hr D. 4.2 hr

Explanation :

Part filled by pipe A in 1 hour = 1/8 Part filled by pipe B in 1 hour = ¼
Part filled by pipe C in 1 hour = 1/24
Part filled by pipe A, pipe B and pipe C in 1 hour
= 1/8+1/4+1/24=10/24
i.e, pipe A, pipe B and pipe C together can fill the tank in 24/10 hours = 2.4 hours

17. Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?

A. 6 min 15 sec B. 5 min 45 sec
C. 5 min 15 sec D. 6 min 30 sec

Explanation :

Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/14
Part filled by pipe A and pipe B in 1 minute = (1/8)+(1/14)=11/56
Pipe A and pipe B were open for 3 minutes Part filled by pipe A and pipe B in 3 minutes = 3x(11/56)
=33/56
Remaining part = 1-(33/56) =23/56
Time taken by pipe B to fill this remaining part = (23/56) + (1/14)
=(23×14) + 56=23/4 minutes = 5 minutes 45 seconds

18. A water tank is two-fifth full. Pipe A can fill a tank in 12 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

A. 2.8 min B. 4.2 min
C. 4.8 min D. 5.6 min

Explanation :

Since pipe B is faster than pipe A, the tank will be emptied.
Part filled by pipe A in 1 minute = 1/12
Part emptied by pipe B in 1 minute = 1/6
Net part emptied by pipe A and pipe B in 1 minute = 1/6-1/12 =1/12
Time taken to empty 2/5 of the tank = (2/5) + (1/12)
=(2×12)+5=4.8 min

19. Pipes A and B can fill a tank in 8 and 24 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. 18 hr B. 6 hr
C. 24 hr D. 12 hr

Explanation :

Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/24
Part emptied by pipe C in 1 minute = 1/12
Net part filled by pipe A, pipe B and pipe C in 1 minute
= (1/8)+(1/24)-(1/12)
=2/24
=1/12
i.e, the tank will be filled in 12minutes

20. One pipe can fill a tank 6 times as fast as another pipe. If together the two pipes can fill the tank in 22 minutes, then the slower pipe alone will be able to fill the tank in:”

A. 164 min B. 154 min C. 134 min D. 144 min

Explanation :

Let the slower pipe alone can fill the tank in x minutes. Then the faster pipe can fill the tank in 6 x minutes
Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 6/x
Part filled by both the pipes in 1 minute = 1/x+6/x
It is given that both the pipes together can fill the tank in 22 minutes
Part filled by both the pipes in 1 minute = 1/22
1/x+6/x=1/22 7=(1/22)x x=22×7=154
i.e., the slower pipe alone fills the tank in 154 minutes

21. Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

A. 3 min B. 2.5 min
C. 2 min D. 1.5 min