Pipes and Cistern
- There are two pumps to fill a tank with water. First pump can fill the empty tank in 8 hours, while the second in 10 hours. If both the pumps are opened at the same time and kept open for 4 hours, the part of tank that will be filled up is:
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As per the given in question , we have
Part of the tank filled in an hour by both pumps = 1 + 1 = 5 + 4 = 9 8 10 40 40
Correct Option: A
As per the given in question , we have
Part of the tank filled in an hour by both pumps = 1 + 1 = 5 + 4 = 9 8 10 40 40 ∴ Part of the tank filled in 4 hours = 4 × 9 = 9 40 10
- A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, (in hours) is
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As per the given in question , we have
Time taken by pipe B = 2x hours
Time taken by pipe A = x hours∴ Time taken by pipe C 
Time taken by pipe C = 4x hours 3 ∴ 1 + 1 + 3 
x 2x 4x ⇒ 4 + 2 + 3 = 3 4x 20
Correct Option: A
As per the given in question , we have
Time taken by pipe B = 2x hours
Time taken by pipe A = x hours∴ Time taken by pipe C Time taken by pipe C = 4x hours 3 ∴ 1 + 1 + 3 x 2x 4x ⇒ 4 + 2 + 3 = 3 4x 20
⇒ 9 × 20 = 4x × 3⇒ x = 9 × 20 = 15 hours 4 × 3
- 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 alternatively, the tank will be full in :
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On the basis of given details in question ,
Part filled by A and B in 1 hour = 1 + 1 = 5 + 4 = 3 .......(i) 12 15 60 20 Part filled by A and C in the next 1 hour = 1 + 1 = 5 + 3 = 2 12 20 60 15 Part filled in 2 hours = 3 + 2 = 9 + 8 = 17 20 15 60 60 ⇒ Part filled in 6 hours = 51 60
Correct Option: C
On the basis of given details in question ,
Part filled by A and B in 1 hour = 1 + 1 = 5 + 4 = 3 .......(i) 12 15 60 20 Part filled by A and C in the next 1 hour = 1 + 1 = 5 + 3 = 2 12 20 60 15 Part filled in 2 hours = 3 + 2 = 9 + 8 = 17 20 15 60 60 ⇒ Part filled in 6 hours = 51 60 Remaining part = 1 - 51 = 9 = 3 60 60 20
This part will be filled by (A+B) in 1 hour. [By (i)]
∴ Total time taken = 7 hours
- A pump can fill a tank with water in 2 hours. Because of a leak in the tank it was
taking 2 1 hours to fill the tank. The leak can drain all the water off the tank in : 3
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As per the given in question , we have
Work done in 1 hour by the filling pump = 1 2 Work done in 1 hour by the leak and the filling pump = 3 7
Correct Option: D
As per the given in question , we have
Work done in 1 hour by the filling pump = 1 2 Work done in 1 hour by the leak and the filling pump = 3 7 ∴ Work done by the leak in 1 hour = 1 - 3 = 7 - 6 = 1 2 7 14 14
Hence, the leak can empty the tank in 14 hours.
- A pipe can fill a tank with water in 3 hours. Due to leakage in bottom, it takes
3 1 hours to fill it . In what time the leak will empty the fully filled tank ? 2
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Let the leak empty the full tank in t hours.
According to question ,1 - 1 = 2 3 t 7 ⇒ 1 = 1 - 2 = 7 - 6 t 3 7 21
Correct Option: B
Let the leak empty the full tank in t hours.
According to question ,1 - 1 = 2 3 t 7 ⇒ 1 = 1 - 2 = 7 - 6 t 3 7 21 ⇒ 1 = 1 ⇒ t = 21 hours t 21
