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Examoogle • User • info@examoogle.com • EE-2024-8821
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A and B can do a piece of work in 10 days, B and C in 12 days and C and A in 15 days. If A, B and C work together, in how many days will they complete the work?
8 days
7 days
5 days
6 days
8 days
Given: Time taken by (A + B) = 10 days, (B + C) = 12 days, and (C + A) = 15 days.
Time taken by (A + B) = 10 days, (B + C) = 12 days, and (C + A) = 15 days.
Time=Combined EfficiencyTotal Work
Find LCM of 10, 12, 15 = 60 (Total Work). Efficiencies: A+B = 6, B+C = 5, C+A = 4. Total = 15. Efficiency of A+B+C = 15/2 = 7.5. Time = 60 / 7.5 = 8 days.
Students sum the individual pair efficiencies (6+5+4=15) and directly calculate 1560=4 days, forgetting to divide 15 by 2 because each person is counted twice.
Assume Total Work using LCM
Take the LCM of the time taken by each pair (10, 12, and 15 days) to find the total units of work.
Total Work=LCM(10,12,15)=60 units
Calculate Pair Efficiencies
Efficiency is the work done per day, given by Efficiency=TimeTotal Work.
Efficiency of (A+B)=1060=6 units/day Efficiency of (B+C)=1260=5 units/day Efficiency of (C+A)=1560=4 units/day
Calculate Combined Efficiency of A, B, and C
Adding all pair efficiencies counts each person twice: 2(A+B+C). Divide by 2 to get the combined daily work of A, B, and C.
2(A+B+C)=6+5+4=15 units/day Efficiency of (A+B+C)=215=7.5 units/day
Find Total Days to Complete Work
Divide the total work by the combined efficiency of A, B, and C working together.
Days required=7.560=8 days
A is correct because when A, B, and C work together, their combined daily efficiency is 7.5 units/day, completing 60 units of total work in exactly 8 days.
Questions involving paired combinations (A+B, B+C, C+A) frequently appear in Time & Work and Pipes & Cisterns; always remember to divide the combined sum by 2 to get the individual sum.