Pipes and Cistern
- 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 8 hours. Find the capacity of the tank.
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From the given question ,
Part of tank filled by inlet pipe in 1 hour = 1 - 1 = 4 - 3 = 1 6 8 24 24
Correct Option: A
From the given question ,
Part of tank filled by inlet pipe in 1 hour = 1 - 1 = 4 - 3 = 1 6 8 24 24
Hence, if there is no leak, the inlet pipe will fill the tank in 24 hours.
∴ Capacity of the tank = 24 × 60 × 4 = 5760 litres
- Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 1 hour, B was opened and after 2 hours from the start of A, C also opened . Find the time in which the cistern is just full ?
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[(A's 1 hour work) + (A + B)'s 1 hour work]
= (1/10) + [(1/10) + (1/12)] = 17/60
Remaining part = 1 - (17/60) = 43/60
Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4Correct Option: D
[(A's 1 hour work) + (A + B)'s 1 hour work]
= (1/10) + [(1/10) + (1/12)] = 17/60
Remaining part = 1 - (17/60) = 43/60
Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4
1/4 part is filled by 3 pipes in 1 hour.
43/60 part will be filled by them in 4 x (43/60) hrs. = 2 hours 52 min.
∴ Total time taken to fill the cistern = 4 hours 52 min.
- Two pipes, P ans Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill ?
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12(1 - t/25) = 3
∴ t = 45/4 = 111/4 minutes
∴ Required answer = 111/4 - 3Correct Option: A
12(1 - t/25) = 3
∴ t = 45/4 = 111/4 minutes
∴ Required answer = 111/4 - 3
= 81/4 minutes
- Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. The time taken to fill the tank is ?
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Part filled in 10 hours = 10 x (1/15 + 1/20 - 1/25) = 23/30
Remaining part = (1 - 23/30) = 7/30
Now, (1/15 + 1/20) part is filled by A and B in 1 hr.
7/30 part be filled them in (60/7) x (7/30) = 2 hrs.Correct Option: A
Part filled in 10 hours = 10 x (1/15 + 1/20 - 1/25) = 23/30
Remaining part = (1 - 23/30) = 7/30
Now, (1/15 + 1/20) part is filled by A and B in 1 hr.
7/30 part be filled them in (60/7) x (7/30) = 2 hrs.
∴ Total time taken to fill the tank = (10 + 2) hrs. = 12 hrs.
- If two 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 the faster pipe take to fill the reservoir ?
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Suppose that one pipe takes N hours to fill the reservoir. Then another pipe takes (N - 10) hours.
∴ 1/N + 1/(N - 10) = 1/12Correct Option: C
Suppose that one pipe takes N hours to fill the reservoir. Then another pipe takes (N - 10) hours.
∴ 1/N + 1/(N - 10) = 1/12
⇒ 12(N - 10 + N) = N(N - 10)
or N2 - 34N + 120 = 0
or (N - 30)(N - 4) = 0
∴ N = 30 or N = 4
So, the faster pipe takes 30 hours to fill the reservoir.
