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A can do a piece of work in 63 hours; B and C together can do it in 48 hours, while A and C together can do it in 36 hours. How long (in hours) will B alone take to do it? 4047
112
114
111
113
112
Find the LCM of 63, 48, and 36, which is 1008. Divide this by each time value to get efficiencies, then isolate B's efficiency.
Time taken by A is 63 hours, (B + C) together is 48 hours, and (A + C) together is 36 hours.
Efficiency=TimeTotalWorkтАЛ, WorkBтАЛ=WorkABCтАЛтИТWorkACтАЛ
Find the LCM of 63, 48, and 36, which is 1008. Divide this by each time value to get efficiencies, then isolate B's efficiency.
Students often add A and C's work to A and B's work instead of finding the specific work rates for individual people.
Calculate LCM and Efficiencies
Find LCM of 63, 48, and 36 to be 1008 units. Efficiency of A = 1008/63=16. Efficiency of (B+C) = 1008/48=21. Efficiency of (A+C) = 1008/36=28.
EAтАЛ=16,EB+CтАЛ=21,EA+CтАЛ=28
Find C's efficiency
Since efficiency of (A+C)=28 and A=16, then C=28тИТ16=12.
ECтАЛ=28тИТ16=12
Find B's efficiency
Since efficiency of (B+C)=21 and C=12, then B=21тИТ12=9.
EBтАЛ=21тИТ12=9
Calculate time taken by B
Time taken by B = Total work / Efficiency of B = 1008/9=112.
TBтАЛ=91008тАЛ=112
A is correct because the calculated time for B to complete the work alone is 112 hours.
This problem uses the same logic as pipe and cistern problems, where filling rates are treated as positive work and emptying rates as negative work.
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