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Pipe A can fill a cistern in 10 hours and Pipe B can fill it in 15 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?
6 ┬аhours
5 ┬аhours
8 ┬аhours
7.5 ┬аhours
6 ┬аhours
Use the product/sum formula: (10├Ч15)/(10+15)=150/25=6 hours. Alternatively, visualize LCM of 10 and 15 as 30 units, where A does 3 units/hr and B does 2 units/hr, totaling 5 units/hr; 30/5=6 hours.
Pipe A fills a cistern in 10 hours. Pipe B fills a cistern in 15 hours.
T=A+BA├ЧBтАЛ
Use the product/sum formula: (10├Ч15)/(10+15)=150/25=6 hours. Alternatively, visualize LCM of 10 and 15 as 30 units, where A does 3 units/hr and B does 2 units/hr, totaling 5 units/hr; 30/5=6 hours.
Many students mistakenly calculate the average as (10+15)/2=12.5 hours, ignoring that rates are additive, not times.
Calculate individual work rates
Let the total capacity be the LCM of 10 and 15, which is 30 units. Pipe A efficiency is 30/10=3 units/hr, and Pipe B efficiency is 30/15=2 units/hr.
EAтАЛ=3,EBтАЛ=2
Determine combined efficiency
When both pipes are opened, their work rates add up.
EtotalтАЛ=3+2=5┬аunits/hr
Calculate total time taken
Divide the total capacity by the combined efficiency to find the total time required.
T=530тАЛ=6┬аhours
A is correct because the combined efficiency of the two pipes results in the cistern being filled in exactly 6 hours.
This concept of 'combined efficiency' is identical to solving 'Time and Work' problems where two people working together finish a task faster than either could alone.
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