Question
Pipes A and B can fill a tank in 12 minutes and 15
minutes, respectively, while outlet pipe C can empty the entire tank in 1 hour. All three pipes are open for 'x' minutes, after which pipe A and pipe C are closed. If the tank is completely filled in 10 minutes, find the value of 'x'.Solution
Let the total capacity of the tank be LCM of (12, 15 and 60) = 60 units Number of units of water filled by pipe A in one minute = 60/12 = 5 units Number of units of water filled by pipe B in one minute = 60/15 = 4 units Number of units of water emptied by pipe C in one minute = 60/60 = 1 unit According to question, (5 + 4 – 1)x + 4(10 – x) = 60 8x + 40 – 4x = 60 4x = 20, x = 5 So, the value of ‘x’ is 5 minutes.
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