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Two pipes P and Q can fill a tank in 20 minutes and 30 minutes respectively. There is a waste pipe which withdraws water at the rate of 8 litres per minute. Now the tank is full and If all the pipes are opened simultaneously the tank is emptied in 60 minutes. Find the capacity of the tank.
- a)60ltr
- b)70ltr
- c)80ltr
- d)90ltr
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two pipes P and Q can fill a tank in 20 minutes and 30 minutes respect...
(1/20 + 1/30 – 1/t)*60 = -1
‘-1’ is taken because the work is negative. T is the time taken by the waste pipe to empty the tank alone. We will t = 10
So capacity = 10*8 = 80ltr
‘-1’ is taken because the work is negative. T is the time taken by the waste pipe to empty the tank alone. We will t = 10
So capacity = 10*8 = 80ltr
Most Upvoted Answer
Two pipes P and Q can fill a tank in 20 minutes and 30 minutes respect...
(1/20 + 1/30 – 1/t)*60 = -1
‘-1’ is taken because the work is negative. T is the time taken by the waste pipe to empty the tank alone. We will t = 10
So capacity = 10*8 = 80ltr
‘-1’ is taken because the work is negative. T is the time taken by the waste pipe to empty the tank alone. We will t = 10
So capacity = 10*8 = 80ltr
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Community Answer
Two pipes P and Q can fill a tank in 20 minutes and 30 minutes respect...
Given information:
- Pipe P can fill the tank in 20 minutes.
- Pipe Q can fill the tank in 30 minutes.
- Waste pipe withdraws water at the rate of 8 liters per minute.
- When all pipes are opened simultaneously, the tank is emptied in 60 minutes.
Let's assume the capacity of the tank is 'C' liters.
Filling Rate of Pipe P:
- Pipe P can fill the tank in 20 minutes.
- So, the filling rate of Pipe P = C/20 liters per minute.
Filling Rate of Pipe Q:
- Pipe Q can fill the tank in 30 minutes.
- So, the filling rate of Pipe Q = C/30 liters per minute.
Rate of the Waste Pipe:
- The waste pipe withdraws water at the rate of 8 liters per minute.
Rate of all Pipes Combined:
- When all pipes are opened simultaneously, the tank is emptied in 60 minutes.
- So, the combined filling rate of all pipes = C/60 liters per minute.
Rate of the Waste Pipe = Combined filling rate of all pipes:
- The waste pipe withdraws water at the rate of 8 liters per minute.
- The combined filling rate of all pipes = C/60 liters per minute.
- Therefore, C/60 = 8 liters per minute.
Solving the above equation for C:
- C/60 = 8
- C = 60 * 8
- C = 480 liters
Therefore, the capacity of the tank is 480 liters, which is option C.
- Pipe P can fill the tank in 20 minutes.
- Pipe Q can fill the tank in 30 minutes.
- Waste pipe withdraws water at the rate of 8 liters per minute.
- When all pipes are opened simultaneously, the tank is emptied in 60 minutes.
Let's assume the capacity of the tank is 'C' liters.
Filling Rate of Pipe P:
- Pipe P can fill the tank in 20 minutes.
- So, the filling rate of Pipe P = C/20 liters per minute.
Filling Rate of Pipe Q:
- Pipe Q can fill the tank in 30 minutes.
- So, the filling rate of Pipe Q = C/30 liters per minute.
Rate of the Waste Pipe:
- The waste pipe withdraws water at the rate of 8 liters per minute.
Rate of all Pipes Combined:
- When all pipes are opened simultaneously, the tank is emptied in 60 minutes.
- So, the combined filling rate of all pipes = C/60 liters per minute.
Rate of the Waste Pipe = Combined filling rate of all pipes:
- The waste pipe withdraws water at the rate of 8 liters per minute.
- The combined filling rate of all pipes = C/60 liters per minute.
- Therefore, C/60 = 8 liters per minute.
Solving the above equation for C:
- C/60 = 8
- C = 60 * 8
- C = 480 liters
Therefore, the capacity of the tank is 480 liters, which is option C.
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