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A and B can complete a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can C alone complete the work?
60 days
30 days
45 days
90 days
60 days
Calculate the total LCM of 12, 15, and 20 (which is 60) to find work units, then find individual efficiencies to solve for C.
Time taken by (A+B) = 12 days, (B+C) = 15 days, (C+A) = 20 days.
2(A+B+C)=121тАЛ+151тАЛ+201тАЛ
Calculate the total LCM of 12, 15, and 20 (which is 60) to find work units, then find individual efficiencies to solve for C.
Students often add the efficiencies and forget to multiply by 2, failing to realize that (A+B+C) represents two of each person.
Calculate Total Work
Assuming total work is the LCM of 12, 15, and 20, which is 60 units.
Work=60┬аunits
Calculate Combined Efficiencies
Efficiencies are: (A+B)=60/12=5, (B+C)=60/15=4, (C+A)=60/20=3. Adding these: 2(A+B+C)=5+4+3=12.
(A+B+C)=212тАЛ=6┬аunits/day
Find C's Efficiency
Subtract the efficiency of (A+B) from the total efficiency (A+B+C) to find C's efficiency.
C=(A+B+C)тИТ(A+B)=6тИТ5=1┬аunit/day
Final Calculation
Time taken by C to complete the work alone is Total┬аWork/CтА▓sefficiency.
Time=160тАЛ=60┬аdays
A is correct because the calculated time for C alone to complete the work is 60 days.
This method of finding individual rates from group rates is identical to solving systems of linear equations in Algebra.
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