1. 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 liters a minute. When the tank is full the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank in liters is
A. 5760 liters
B. 1000 liters
B. 1000 liters
C. 1050 liters
D. 3000 liters
D. 3000 liters
2. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half-full and both tanks are opened together, the tank will be:
A. 6 min
B. 8 min
B. 8 min
C. 15 min
D. 30 min
D. 30 min
3. A cistern has two taps which fill it in 12 min and 15 min respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will waste pipe take to empty the full cistern?
A. 6 min
B. 8 min
B. 8 min
C. 10 min
D. 30 min
D. 30 min
4. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the 3 are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?
A. 6 min
B. 8 min
B. 8 min
C. 15 min
D. 10 min
D. 10 min
5. A water tank is two – fifth full. Pipe A can fill a tank in 10 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. 6 min
B. 8 min
B. 8 min
C. 15 min
D. 10 min
D. 10 min
6. Pipes A and B take 20 and 30 minutes to fill a tank respectively. The 2 together will take:
A. 6 min
B. 8 min
B. 8 min
C. 12 min
D. 10 min
D. 10 min
7. Two 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?
A. 1 hour
B. 20 hours
B. 20 hours
C. 6 hours
D. 8 hours
D. 8 hours
8. Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?
A. 1 hour
B. 2 hours
B. 2 hours
C. 6 hours
D. 5 hours
D. 5 hours
9. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
10. 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. 11/17 hour
B. 12/17 hours
B. 12/17 hours
11. A pump can fill a tank with water in 2 hours. Because of la leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
A. 14 hour
B. 12 hours
B. 12 hours
C. 16 hours
D. 15 hours
D. 15 hours
12. Two pipes A and B can fill a cistern in (37 1/2) minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A. 5 min.
B. 9 min.
B. 9 min.
C. 10 min.
D. 15 min.
D. 15 min.
13. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank at the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
A. 6 hours
B. 10 hours
B. 10 hours
C. 15 hours
D. 30 hours
D. 30 hours
14. 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
B. 100 gallons
C. 120 gallons
D. 180 gallons
D. 180 gallons
15. A tank is filled in 5 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. 20 hours
B. 25 hours
B. 25 hours
C. 35 hours
D. Cannot be determined
D. Cannot be determined
E. None of these
16. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
A. 1 hour
B. 2 hours
B. 2 hours
C. 6 hours
D. 8 hours
D. 8 hours
17. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A. 12 min
B. 15 min
B. 15 min
C. 25 min
D. 50 min
D. 50 min
18. 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
B. 11 min 45 sec
C. 12 min 30 sec
D. 14 min 40 sec
D. 14 min 40 sec
19. 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
B. 108 min
C. 144 min
D. 192 min
D. 192 min
20. 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
B. 20 min
C. 27.5 min
D. 30 min
D. 30 min
21. 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 was taken to fill the tank completely?
A. 3 hrs 15 min
B. 3 hrs 45 min
B. 3 hrs 45 min
C. 4 hrs
D. 4 hrs 15 min
D. 4 hrs 15 min
22. 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. 14 hour
B. 7 hours
C. 16 hours
D. 15 hours
D. 15 hours
23. 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
24. If two pipes function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir?A. 30 hour
B. 12 hours
C. 16 hours
D. 15 hours
25. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?
A. 141 hour
B. 121 hours
C. 112 hours
D. 151 hours
Answers
1. Time taken to fill the tank is 1/6 hour
Time taken to empty the tank is 1/8
Work done by the inlet in 1 hour = (1/6 – 1/8) = 1/24
For 1 minute = 1/24 x 1/60 = 1/1440
An inlet pipe fill water at the rate of 4 liters a minute = 1440 x 4 = 5760 liters
2. Time taken to fill the tank in = 1/16 min
Time is taken to empty the tank in = 1/8 min
Work done by both in 1 min = (1/16 – 1/8) = -1/16 (-ve means empty)
Now full tank will be emptied by them in 16 min
Half tank will be emptied in 8 min.
3. C’s work = (A+B+C)’s work – (A+B)’s work
A + B = 1/x + 1/y
So, To fill the cistern = (1/12 + 1/15) = 3/20
Work done by waste pipe in 1 min = work done by all the three taps – work done by two taps
= 1/20 – 3/20 = -2/20 = -1/10
Waste pipe will empty the full cistern in 10 minutes.
4. Work done by the waste pipe in 1 min
= (1/20) - (1/12) + (1/15) = -1/10 [negative sign means emptying]
therefore the waste pipe will empty the full cistern in 10 min
5. Water level in the tank is 2/5
Both the pipes are open = (10 - 6) / (10 x 6) = 1/15
Therefore 2/5 x 15 = 6 minutes
6. Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A+B) in 1 min = 1/20 + 1/30 = 1/12
So both pipes can fill the tank in 12 mins
7. Part filled by A in 1 hour = (1/36)
Part filled by B in 1 hour = (1/45)
Part filled by (A + B) In 1 hour = (1/36) + (1/45) = (9/180) = (1/20)
Hence, both the pipes together will fill the tank in 20 hours.
8. It’s an alternate hour’s problem
A’s 1 hour work = 1/6
B’s 1 hour work = 1/4
A + B means 2 hours of work
(A+B)’s 2 hours work when opened alternately = 1/6 + 1/4 = 5/12
(A+B)’s 4 hours work when opened alternately = 2 (5/12) = 5/6
Remaining = 1 - 5/6 =1/6
It is A’s turn and 1/6 part is filled by A in 1 hour
Total time taken to fill the tank = (4+1) hours = 5 hours
9. Part filled by (A + B + C) in 3 minutes = 3 x (1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
∴ Required ratio = 3/10 x 20/11 = 6/11
10. Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hours.
11. Work done by the leak in 1 hour = 1/2 - 3/7 = 1/14
Leak will empty the tank in 14 hrs.
12.
13. Suppose, first pipe take x hours to fill the tank then
B & C will take (x - 5) and (x - 9) hours respectively.
Therefore, 1/x +1/(x - 5) = 1/(x - 9)
On solving, x = 15
Hence, time required by first pipe is 15 hours.
14. Work done by the waste pipe in 1 minute =
1/15 - (1/20 + 1/24) - (1/15 - 11/120) = -1/40 [-ve means emptying]
Volume of 1/40 part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons
15. Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
⇒ 1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
⇒ x = 35 hrs
16. Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
∴ 1/x + 1/(x+6) = 1/4 ⇔ (x + 6 + x)/(x * (x + 6)) = 1/4
⇔ x2 - 2x -24 = 0 ⇔ (x - 6) (x + 4) = 0
⇔ x = 6 hours [Ignoring the -ve value of x]
17. Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A + B) in 1 min = 1/20 + 1/30 = 1/12
∴ Both the pipes can fill the tank in 12 minutes.
18. 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
1/20 : 8/15 :: 1 : x
x = 8/15 x 1 x 20 = 10 2/3 min = 10 min. 40 sec.
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
19. 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 = 144min
20. Part filled by (A + B) in 1 minute = 1/60 + 1/40 = 1 24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
=> x/2 x 1/15 = 1
=> x = 30 min.
21. Time taken by one tap to fill half the tank = 3hrs.
Part filled by the four taps in 1 hour = (4×1/6)
= 2/3.
Remaining part = (1 - 1/2)
= 1/2.
Therefore, 2/3 : 1/2 :: 1 : x
=> x = (1/2×1×3/2)
=> x = 3/ 4 hrs i.e 45 mins.
So, the total time taken = 3 hrs 45 min.
22.
23. (A+B+C) - (A+B) can give you the answer.
(A+B+C) =1/6 and (A+B+C) in 2 hrs = 2/6 and remaining part 1-2/6 = 2/3.
So (A+B) in 7 hrs is 2/ (3x7) = 2/21.
(1/6 - 2/21) = 1/14 so answer is 14.
24. let the reservoir be filled by first pipe in x hours.
Then ,second pipe fill it in (x+10)hrs.
Therefore (1/x)+(1/x+10) = (1/12)
(x+10+x)/(x(x+10)) = (1/12).
x^2 –14x-120=0
(x-20)(x+6)=0
x=20 [neglecting the negative value of x]
so, the second pipe will take (20+10)hrs. (i.e) 30 hours to fill the reservoir
25. Work done by the two pipes in 1 hour =(1/14) + (1/16)=(15/112).
Time taken by these pipes to fill the tank = (112/15) hrs = 7 hrs 28 min.
Due to leakage, time taken = 7 hrs 28 min + 32 min = 8 hrs
Work done by (two pipes + leak) in 1 hour = (1/8).
Work done by the leak m 1 hour = (15/112) - (1/8) = (1/112).
Leak will empty the full cistern in 112 hours.