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P and Q can finish a piece of work in 12 days and 18 days respectively. If they work together, how many days will they take to complete the work?
7.2 days
8.5 days
6.4 days
9.0 days
7.2 days
Use the product-over-sum formula directly for two workers to calculate total time in seconds.
P can finish a piece of work in 12 days and Q can finish it in 18 days.
T=x+yx├ЧyтАЛ
Use the product-over-sum formula directly for two workers to calculate total time in seconds.
Students often average the days or add them up directly instead of combining their work rates.
Find Total Work via LCM
Assume the total work is the LCM of the individual days: LCM(12,18)=36 units.
Total┬аWork=36┬аunits
Calculate Individual Efficiencies
P's daily output is 36/12=3 units and Q's daily output is 36/18=2 units.
EPтАЛ=3,EQтАЛ=2
Calculate Combined Efficiency
When working together, add their individual efficiencies to find the total daily output.
EtotalтАЛ=3+2=5┬аunits/day
Calculate Total Time Taken
Divide the total work by the combined efficiency to get the required days.
T=536тАЛ=7.2┬аdays
A is correct because working together they complete the work in 7.2 days.
This concept directly applies to Pipes and Cisterns problems where filling and emptying rates function identically to work efficiencies.
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