Question
Two taps can fill a tank in 18 hours and 24 hours,
respectively. A waste pipe can empty the tank in 36 hours. If all three pipes are opened together, how much time will it take to fill the tank 75% of its capacity?Solution
Rate of the first tap = 1/18 per hour Rate of the second tap = 1/24 per hour Rate of the waste pipe = -1/36 per hour Net rate = (1/18) + (1/24) - (1/36) LCM of 18, 24, and 36 = 72 Net rate = (4/72) + (3/72) - (2/72) = 5/72 Time to fill the tank fully = 1 ÷ (5/72) = 72/5 = 14.4 hours Time to fill 75% = 14.4 × 0.75 = 10.8 hours Correct Option: a.
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