A and B can complete a piece of work in 80 days and 120 days respectively. They started working together but A left after 20 days. After another 12 days C joined B and they completed the work in 28 more days. In how many days can C alone complete the work ?
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110 days
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112 days
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114 days
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120 days
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90 days
B
Correct answer
Explanation
A=80, B=120. LCM=240. A=3, B=2. Together for 20 days: (3+2)*20 = 100. Remaining = 140. B works for 12 more days: 2*12 = 24. Remaining = 116. B and C work for 28 days: (2+C)*28 = 116. 2+C = 116/28 = 4.14. This doesn't result in 112. Let's re-read: A left after 20 days. B worked for 20+12+28 = 60 days. B's work = 60*2 = 120. A's work = 20*3 = 60. Total = 180. C's work = 240-180 = 60. C worked for 28 days. C's rate = 60/28 = 15/7. Time = 240 / (15/7) = 112.