Question
John, Emily, and Michael can each complete a task in 15
days, 20 days, and 18 days, respectively. They decide to work on the task alternately, starting with John, followed by Emily, and then Michael for 15 days. The remaining work is handled by Michael alone. Calculate the total time taken to complete the entire task using this alternating work pattern.Solution
ATQ, Let the total work = 180 units {LCM of 15, 20 and 18} Efficiency of ‘John’ = (180/15) = 12 units/day Efficiency of ‘Emily’ = (180/20) = 9 units/day Efficiency of ‘Michael’ = (180/18) = 10 units/day So, work completed in 3 days = (12 + 9 + 10) = 31 units Work completed in 15 days = 31 × 5 = 155 units Time taken by ‘C’ to complete the remaining work = (180 – 155)/10 = 2.5 days Therefore, total time taken = 15 + 2.5 = 17.5 days
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