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Three pipes A, B and C are opened to fill a tank such that B and C can fill the tank alone for 18 hours and 12 hours, respectively, while pipe A can empty a fully filled tank in 15 hours. All the three pipes are opened together, and after 5 hours pipe A is closed. In how many hours will the remaining tank be filled?
1 hour 15 minutes
1 hour 45 minutes
4 hours 36 minutes
2 hours 50 minutes
4 hours 36 minutes
Calculate LCM of times to find total capacity. Determine the net work done per hour by all pipes, multiply by the duration of simultaneous operation, subtract from capacity, then divide remaining work by the rate of the pipes left open.
Pipes B and C fill a tank in 18 and 12 hours, respectively. Pipe A empties it in 15 hours. All opened together for 5 hours, then A is closed.
Total┬аWork=LCM(18,12,15)=180 units, RatenetтАЛ=RBтАЛ+RCтАЛтИТRAтАЛ=10+15тИТ12=13 units/hour
Calculate LCM of times to find total capacity. Determine the net work done per hour by all pipes, multiply by the duration of simultaneous operation, subtract from capacity, then divide remaining work by the rate of the pipes left open.
Many students subtract A's emptying rate from the total capacity instead of the net rate, or forget to identify that B and C are still filling after A closes.
Calculate Total Capacity
Find the LCM of 18, 12, and 15 to represent the total volume of the tank.
LCM(18,12,15)=180┬аunits
Calculate Hourly Rates
Efficiency of pipe B is 180/18=10, C is 180/12=15, and A is 180/15=12 (negative).
RBтАЛ=10,RCтАЛ=15,RAтАЛ=тИТ12
Work Done in 5 Hours
Net rate with A, B, and C open is 10+15тИТ12=13. In 5 hours, work done is 13├Ч5=65.
W1тАЛ=13├Ч5=65┬аunits
Calculate Remaining Time
Remaining capacity is 180тИТ65=115. Only B and C work now at rate 10+15=25. Time taken is 115/25=4.6 hours.
Time=25115тАЛ=4.6┬аhours=4┬аhours┬а36┬аminutes
C is correct because the remaining 115 units of capacity filled by pipes B and C at 25 units/hour takes exactly 4 hours and 36 minutes.
This is essentially a 'Work, Efficiency and Time' problem; treat filling pipes as positive work and emptying pipes as negative work, exactly like people completing or destroying a project.
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