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One pipe can fill the tank in 14 min, while another pipe can empty the completely filled tank in 63 min. If both the pipes are operated together on empty tank, how long (in min) will it take to fill one-third of the tank? 3939
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Use the LCM of 14 and 63 (which is 126) as the capacity. Net efficiency is (126/14) - (126/63) = 9 - 2 = 7 units/min. Target work is 1/3 of 126, which is 42 units.
Pipe A fills in 14 min, Pipe B empties in 63 min.
Time=Net┬аEfficiencyTotal┬аWorkтАЛ
Use the LCM of 14 and 63 (which is 126) as the capacity. Net efficiency is (126/14) - (126/63) = 9 - 2 = 7 units/min. Target work is 1/3 of 126, which is 42 units.
Students often calculate the time to fill the full tank (126/7 = 18 min) instead of reading the requirement for one-third of the tank.
Calculate Net Efficiency
Let total capacity be the LCM of 14 and 63, which is 126 units. Efficiency of filling pipe A = 126 / 14 = 9 units/min. Efficiency of emptying pipe B = 126 / 63 = 2 units/min. Net efficiency when both operate = 9 - 2 = 7 units/min.
Net┬аEfficiency=9тИТ2=7┬аunits/min
Determine Target Work
We need to find the time to fill one-third of the tank capacity.
Target┬аWork=31тАЛ├Ч126=42┬аunits
Calculate Time Required
Divide the target work by the net efficiency to find the total time taken.
Time=742тАЛ=6┬аmin
A is correct because the net efficiency of 7 units per minute fills 42 units of the tank in exactly 6 minutes.
This LCM method for work efficiency is identical to solving 'Time and Work' problems where one person helps and another hinders the progress.
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