There are two taps to fill a tank while a third to empty it. When the third tap is closed, they can fill the tank in 10 minutes respectively. If all the three taps be opened, the tank is filled in 15 minutes. If the first two taps are closed, in what time can the third tap empty the tank when it is full? I want answer with explanation .

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Answers

2016-03-29T17:55:40+05:30
Let the taps that fill the tank be A and B and the tap which empties the tank be C.
time taken by A and B to fill the tank when C is closed = 10 min
amount of tank that can be filled in 1 min = 1/10
time taken by the tank to get filled when all three taps are opened = 15 min
amount of tank that can be filled in 1 min when all three taps are opened =1/15
volume of tank that can be filled in 1 min when all three taps are opened = volume of tank that can be filled in 1 min when C is closed - volume of tank that can be emptied when A and B are closed in 1 min
1/15 = 1/10 - x
x = 1/10 - 1/15 = 1/30
volume of tank that can be emptied when A and B are closed in 1 min = 1/30
volume of tank that can be emptied when A and B are closed = 30 min
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