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A tap can fill a tank in 24 hours, while another tap can empty the full tank in 36 hours. If both taps are opened together in an empty tank, in how many hours will the tank be completely filled?
72 ┬аhours
60 ┬аhours
48 ┬аhours
36 ┬аhours
72 ┬аhours
Use the LCM method: LCM of 24 and 36 is 72. Efficiency of filling tap = +3 units/hr, emptying tap = -2 units/hr. Net efficiency = 1 unit/hr. Time = Total Capacity / Net Efficiency.
Tap A fills a tank in 24 hours, Tap B empties the tank in 36 hours.
T=yтИТxxyтАЛ
Use the LCM method: LCM of 24 and 36 is 72. Efficiency of filling tap = +3 units/hr, emptying tap = -2 units/hr. Net efficiency = 1 unit/hr. Time = Total Capacity / Net Efficiency.
Many students add the rates (24 + 36) instead of subtracting the emptying rate from the filling rate, which leads to incorrect results.
Determine Capacity
Assume the total capacity of the tank is the Least Common Multiple (LCM) of 24 and 36.
LCM(24,36)=72┬аunits
Calculate Efficiencies
Calculate the work done by each tap per hour. Tap A fills 3 units/hr and Tap B empties 2 units/hr.
RateAтАЛ=2472тАЛ=3,RateBтАЛ=тИТ3672тАЛ=тИТ2
Calculate Combined Work
When both are open, the net rate is the sum of the filling and emptying rates.
Net┬аRate=3тИТ2=1┬аunit/hr
Final Time Calculation
Divide the total capacity by the net rate of work.
Time=172тАЛ=72┬аhours
A is correct because the net efficiency of 1 unit/hour applied to a 72-unit tank results in 72 hours.
This concept is identical to problems involving negative work in physics, such as a battery being drained while it is being charged.
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