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Pipe A can fill a tank in 3 hours, pipe B can fill the same tank in 15 hours and pipe C can fill the same tank in 10 hours. The time taken (in hours) by them to fill half of the same tank if they operate together is: 1190
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Find the LCM of 3, 15, and 10, which is 30. Calculate individual efficiencies: A=10, B=2, C=3. Total efficiency = 15. Time for full tank = 30/15 = 2. Half tank = 2/2 = 1 hour.
Pipe A fills in 3 hours, Pipe B in 15 hours, and Pipe C in 10 hours.
T=EfficiencyAтАЛ+EfficiencyBтАЛ+EfficiencyCтАЛTotal┬аWorkтАЛ
Find the LCM of 3, 15, and 10, which is 30. Calculate individual efficiencies: A=10, B=2, C=3. Total efficiency = 15. Time for full tank = 30/15 = 2. Half tank = 2/2 = 1 hour.
Many students calculate the time for the full tank (2 hours) and forget to divide by 2 for the 'half of the same tank' requirement.
Calculate Total Capacity and Efficiency
Assume total capacity is the LCM of 3, 15, and 10, which is 30 units. The efficiencies are: Efficiency of A = 30/3=10, Efficiency of B = 30/15=2, Efficiency of C = 30/10=3.
Total┬аEfficiency=10+2+3=15┬аunits/hour
Calculate Time for Full Tank
The time taken to fill the entire tank is the total capacity divided by the combined efficiency of the three pipes.
TimeFullтАЛ=1530тАЛ=2┬аhours
Calculate Time for Half Tank
Since we need to fill only half of the tank, the required time is half of the time taken to fill the full tank.
TimeHalfтАЛ=22тАЛ=1┬аhour
B is correct because the combined work rate fills the tank in 2 hours, meaning half the tank is filled in 1 hour.
This concept is identical to 'Time and Work' problems where individuals work together; the only difference is substituting 'pipes' for 'men' and 'tank capacity' for 'total units of work'.
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