Question
Carol, Bruce, and Peter can decorate a venue in 7, 14,
and 21 days respectively. If they start working together, but Carol leaves 3 days before completion, Bruce leaves 1 day before, and Peter stays till the end, how many days does it take to complete the decoration?Solution
Carol, Bruce, and Peter can decorate a venue in 7, 14, and 21 days respectively. LCM of 7,14, and 21 =42. Total work =42units The efficiency of Carol =42/7 = 6 units. The efficiency of Bruce =42/14=3 units The efficiency of Peter =42/21=2 units. Suppose the work had not been left by Carol and Bruce. Extra work =6×3+3×1=21 units Total work =42+21 =63units. Time =63/11 =5(8/11) days.
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