Question 69

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 and 12 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?

Solution

Let the capacity of tank be 180 litres.

1st tap fill 180 litres in 10 minutes, 1min= 18 lt fill

2nd tap fill 180 litres in 12 minutes, 1min= 15 lt fill

3rd tap empty 180 litres in x minutes [let]... 1 min empty = 180/x lt

Total filling time = 15 minutes

15*18 + 15*15 - 15*180/x = 180

270 + 225 - 2700/x = 180

2700/x = 315

x = 2700/315

x = 8 min and 34 secs

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