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Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively while a third pipe R can empty the tank in 30hrs. If all the pipes are opened together for 10hrs and then pipe R is closed then in what time the tank can be filled.
- a)400/23hrs
- b)400/27hrs
- c)200/23hrs
- d)200/27hrs
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively whil...
(1/20 + 1/25 – 1/30)*10 + (1/20 + 1/25)*x = 1
We get x = 130/27, so total time to fill the tank = 130/27 + 10 = 400/27 hrs
We get x = 130/27, so total time to fill the tank = 130/27 + 10 = 400/27 hrs
Most Upvoted Answer
Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively whil...
Given:
Pipe P can fill the tank in 20 hours
Pipe Q can fill the tank in 25 hours
Pipe R can empty the tank in 30 hours
All pipes were opened together for 10 hours and then pipe R was closed.
To find:
In how much time the tank can be filled.
Solution:
Let us assume the capacity of the tank to be 100 units.
Pipe P can fill 5 units/hour (100/20)
Pipe Q can fill 4 units/hour (100/25)
Pipe R can empty 3.33 units/hour (100/30)
When all pipes are opened together for 10 hours, the net inflow into the tank is:
Inflow = (P+Q-R)*10
Inflow = (5+4-3.33)*10
Inflow = 16.7 units
After 10 hours, let x hours be required to fill the remaining part of the tank.
So, the remaining part of the tank will be:
Remaining part of the tank = (100 - 16.7) = 83.3 units
Now, only pipes P and Q will be opened for x hours.
Inflow by P and Q = (P+Q)*x
Inflow by P and Q = (5+4)*x
Inflow by P and Q = 9x
Now, the inflow and outflow are equal when the tank is filled.
So, we can write:
Inflow by P and Q = Outflow by R
9x = 3.33(10)
x = 37.8 hours
Therefore, the total time taken to fill the tank = 10 + 37.8 = 47.8 hours
Hence, the correct option is (B) 400/27 hours.
Pipe P can fill the tank in 20 hours
Pipe Q can fill the tank in 25 hours
Pipe R can empty the tank in 30 hours
All pipes were opened together for 10 hours and then pipe R was closed.
To find:
In how much time the tank can be filled.
Solution:
Let us assume the capacity of the tank to be 100 units.
Pipe P can fill 5 units/hour (100/20)
Pipe Q can fill 4 units/hour (100/25)
Pipe R can empty 3.33 units/hour (100/30)
When all pipes are opened together for 10 hours, the net inflow into the tank is:
Inflow = (P+Q-R)*10
Inflow = (5+4-3.33)*10
Inflow = 16.7 units
After 10 hours, let x hours be required to fill the remaining part of the tank.
So, the remaining part of the tank will be:
Remaining part of the tank = (100 - 16.7) = 83.3 units
Now, only pipes P and Q will be opened for x hours.
Inflow by P and Q = (P+Q)*x
Inflow by P and Q = (5+4)*x
Inflow by P and Q = 9x
Now, the inflow and outflow are equal when the tank is filled.
So, we can write:
Inflow by P and Q = Outflow by R
9x = 3.33(10)
x = 37.8 hours
Therefore, the total time taken to fill the tank = 10 + 37.8 = 47.8 hours
Hence, the correct option is (B) 400/27 hours.
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Community Answer
Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively whil...
(1/20 + 1/25 – 1/30)*10 + (1/20 + 1/25)*x = 1
We get x = 130/27, so total time to fill the tank = 130/27 + 10 = 400/27 hrs
We get x = 130/27, so total time to fill the tank = 130/27 + 10 = 400/27 hrs
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Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively while a third pipe R can empty the tank in 30hrs. If all the pipes are opened together for 10hrs and then pipe R is closed then in what time the tank can be filled.a)400/23hrsb)400/27hrsc)200/23hrsd)200/27hrse)None of theseCorrect answer is option 'B'. Can you explain this answer?
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