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A and B together can complete a task in 10 days, B and C in 12 days and A and C in 15 days. How long will A, B and C take to complete the task working together?
7 days
10 days
8 days
9 days
8 days
Calculate the LCM of (10, 12, 15) to get 60 units of work. Sum the efficiencies: (A+B)=6, (B+C)=5, (A+C)=4. Sum = 15 units per 2 cycles. Divide total work by half the sum of efficiencies.
Time taken by (A+B) = 10 days, (B+C) = 12 days, and (A+C) = 15 days.
Time=EfficiencyTotalWorkтАЛ
Calculate the LCM of (10, 12, 15) to get 60 units of work. Sum the efficiencies: (A+B)=6, (B+C)=5, (A+C)=4. Sum = 15 units per 2 cycles. Divide total work by half the sum of efficiencies.
Students often forget to divide the combined efficiency by 2, as each person (A, B, and C) is counted twice in the sum (A+B, B+C, A+C).
Calculate Total Work
Assuming the total work is the Least Common Multiple (LCM) of the given days: 10, 12, and 15.
LCM(10,12,15)=60┬аunits
Calculate Individual Efficiencies
Determine the efficiency of each pair: (A+B) = 60/10 = 6, (B+C) = 60/12 = 5, (A+C) = 60/15 = 4.
(A+B)+(B+C)+(C+A)=6+5+4=15
Determine Combined Efficiency of A, B, and C
Since each person is added twice, divide the total efficiency by 2.
2(A+B+C)=15тЯ╣(A+B+C)=215тАЛ=7.5
Calculate Time Taken
Divide the total work by the combined efficiency of A, B, and C.
Time=7.560тАЛ=8┬аdays
C is correct because the combined efficiency of A, B, and C is 7.5 units/day, resulting in a time of 8 days to complete 60 units of work.
This 'doubling' concept is identical to solving problems involving multi-stage gear systems or current division in circuits where components are counted in parallel branches.
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