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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern.
Quantity I: Due to leakage, time taken to fill the tank
Quantity II: Time taken to empty the full cistern
Quantity II: Time taken to empty the full cistern
- a)Quantity I > Quantity II
- b)Quantity I < Quantity II
- c)Quantity I ≥ Quantity II
- d)Quantity I ≤ Quantity II
- e)Quantity I = Quantity II or relation cannot be established
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 12 hours and 18 hours respectivel...
Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108).
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken to fill the tank = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken to fill the tank = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.
Most Upvoted Answer
Two pipes A and B can fill a tank in 12 hours and 18 hours respectivel...
Quantity I: Due to leakage, time taken to fill the tank
Let the capacity of the tank be C.
Pipe A can fill the tank in 12 hours, so in 1 hour it can fill 1/12th of the tank.
Pipe B can fill the tank in 18 hours, so in 1 hour it can fill 1/18th of the tank.
When both pipes are opened together, they can fill the tank in x hours. So, in 1 hour, they can fill 1/xth of the tank.
Using the formula, Work = Rate x Time, we can write:
Work done by pipe A in x hours = (1/12) * x
Work done by pipe B in x hours = (1/18) * x
Work done by both pipes in x hours = (1/x) * x = 1
But due to leakage, the tank is filled in (x + 48/60) hours. So, we can write:
(1/12) * x + (1/18) * x = 1 * (x + 48/60)
Simplifying this equation, we get:
x = 16
So, the tank can be filled in 16 hours when both pipes are open and there is leakage. But we need to find the time taken to fill the tank due to leakage, which is 48 minutes (or 0.8 hours).
Therefore, Quantity I is 0.8 hours.
Quantity II: Time taken to empty the full cistern
This quantity is not related to the given information and cannot be determined from the given data.
Hence, the answer is (a) Quantity I.
Let the capacity of the tank be C.
Pipe A can fill the tank in 12 hours, so in 1 hour it can fill 1/12th of the tank.
Pipe B can fill the tank in 18 hours, so in 1 hour it can fill 1/18th of the tank.
When both pipes are opened together, they can fill the tank in x hours. So, in 1 hour, they can fill 1/xth of the tank.
Using the formula, Work = Rate x Time, we can write:
Work done by pipe A in x hours = (1/12) * x
Work done by pipe B in x hours = (1/18) * x
Work done by both pipes in x hours = (1/x) * x = 1
But due to leakage, the tank is filled in (x + 48/60) hours. So, we can write:
(1/12) * x + (1/18) * x = 1 * (x + 48/60)
Simplifying this equation, we get:
x = 16
So, the tank can be filled in 16 hours when both pipes are open and there is leakage. But we need to find the time taken to fill the tank due to leakage, which is 48 minutes (or 0.8 hours).
Therefore, Quantity I is 0.8 hours.
Quantity II: Time taken to empty the full cistern
This quantity is not related to the given information and cannot be determined from the given data.
Hence, the answer is (a) Quantity I.
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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern.Quantity I: Due to leakage, time taken to fill the tankQuantity II: Time taken to empty the full cisterna)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'B'. Can you explain this answer?
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