Pipes and Cistern
- A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak ?
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From the given question ,
∴ Part of the cistern filled by pipe in 1 hour = 1 9 Due to a leakage ,Part of the cistern filled by pipe in 1 hour = 1 10 Part of the tank emptied by the leak in 1 hour = 1 - 1 9 10
Correct Option: C
From the given question ,
∴ Part of the cistern filled by pipe in 1 hour = 1 9 Due to a leakage ,Part of the cistern filled by pipe in 1 hour = 1 10 Part of the tank emptied by the leak in 1 hour = 1 - 1 9 10 Part of the tank emptied by the leak in 1 hour = 10 - 9 = 1 90 90
∴ Required time = 90 hours
- Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time (in hours) in which the tank can be filled by pipe C alone is
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On the basis of given details in question ,
∴ Part of the tank filled by (A + B + C) in 1 hour = 1 6 Part of tank filled by these in 2 hours = 2 = 1 6 3 Remaining part = 1 - 1 = 2 3 3 Time taken by A and B in filling 2 rd part = 8 hours 3 ∴ Time taken by A and B in filling the whole tank = 8 × 3 = 12 hours 2
Correct Option: B
On the basis of given details in question ,
∴ Part of the tank filled by (A + B + C) in 1 hour = 1 6 Part of tank filled by these in 2 hours = 2 = 1 6 3 Remaining part = 1 - 1 = 2 3 3 Time taken by A and B in filling 2 rd part = 8 hours 3 ∴ Time taken by A and B in filling the whole tank = 8 × 3 = 12 hours 2 ∴ Part of tank filled by C in an hour = 1 - 1 = 1 6 12 12
Hence, required time = 12 hours
- Two pipes A and B can fill a tank in 6 hours and 8 hours respectively. If both the pipes are opened together, then after how many hours should B be closed so that the tank is full in 4 hours?
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As per the given in question , we have
Part of the tank filled in 4 hours by pipe A = 4 = 2 6 3 Remaining part = 1 - 2 = 1 3 3 Time taken by pipe B in filling 1 part = 8 hours 3 3
We can find required answer with the help of given formula :
Here, p = 6,q = 8, t = 4Required time = q 1 - t p
Correct Option: D
As per the given in question , we have
Part of the tank filled in 4 hours by pipe A = 4 = 2 6 3 Remaining part = 1 - 2 = 1 3 3 Time taken by pipe B in filling 1 part = 8 hours 3 3
We can find required answer with the help of given formula :
Here, p = 6,q = 8, t = 4Required time = q 1 - t p Required time = 8 1 - 4 6 Required time = 8 hours 3
- Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened simultaneously, but after two hours, pipe A is closed. How many hours will B take to fill the remaining part of the cistern ?
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On the basis of given details in question ,
Part of the cistern filled in 2 hours by pipe A and B = 2 1 + 1 = 2 4 + 3 = 7 6 8 24 12 Remaining part = 1 - 7 = 5 12 12
Correct Option: B
On the basis of given details in question ,
Part of the cistern filled in 2 hours by pipe A and B = 2 1 + 1 = 2 4 + 3 = 7 6 8 24 12 Remaining part = 1 - 7 = 5 12 12 ∴ Time taken by pipe B in filling 5/12 part = 5 × 8 = 10 = 3 1 hours. 12 3 3
- A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in :
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According to question , we have
Part emptied by the leak in 1 hour = 1 - 1 = 5 - 4 = 1 8 10 40 40
Correct Option: D
According to question , we have
Part emptied by the leak in 1 hour = 1 - 1 = 5 - 4 = 1 8 10 40 40
∴ The leak will empty the cistern in 40 hours.