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Pipe A can fill a tank in 12 hours, pipe B in 15 hours, and an outlet C can empty it in 20 hours. A and B are opened together for 5 hours, and then C is also opened. Find the total time to fill the tank.
7.5 hours
6 hours
5.5 hours
6.5 hours
7.5 hours
Calculate LCM (60). Efficiency of A+B+C = 5+4-3 = 6 units/hr. Total time = (Remaining capacity / combined efficiency) + time already spent.
Pipe A fills in 12h, Pipe B in 15h, Outlet C empties in 20h. A and B work for 5 hours, then C joins.
Total┬аCapacity=LCM┬аof┬аtime┬аperiods, Efficiency=TimeTotalCapacityтАЛ
Calculate LCM (60). Efficiency of A+B+C = 5+4-3 = 6 units/hr. Total time = (Remaining capacity / combined efficiency) + time already spent.
Students often forget to subtract the efficiency of the outlet pipe C, or they mistakenly include C in the first 5 hours of work.
Determine total capacity and efficiencies
Assume total capacity is the LCM of 12, 15, and 20, which is 60 units. Efficiency of A = 60/12 = 5 units/hr, B = 60/15 = 4 units/hr, and C = -60/20 = -3 units/hr.
EffA+BтАЛ=5+4=9,EffA+B+CтАЛ=5+4тИТ3=6
Calculate work done in first 5 hours
Pipes A and B operate for 5 hours at a combined rate of 9 units/hr.
WorkinitialтАЛ=9├Ч5=45┬аunits
Calculate remaining work and time for C
Remaining capacity to fill is 60 - 45 = 15 units. When C is opened, the net efficiency becomes 6 units/hr.
TimeremainingтАЛ=615тАЛ=2.5┬аhours
Calculate total time
Total time is the sum of the initial 5 hours and the subsequent 2.5 hours.
Total┬аTime=5+2.5=7.5┬аhours
A is correct because the total time taken to fill the tank is 7.5 hours.
This LCM efficiency method is universal; it applies to all 'Work and Time' problems, including men-women-children labor tasks.
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