Question
"A" can finish a task by himself in 30 days. "B" is
twice as efficient as "C" and three times more efficient than "A". If "A" and "C" begin the task together, after how many days should "B" take over to ensure the task is completed in precisely 11 days?Solution
Let the total work be 60 units. So, efficiency of 'A' = 60 ÷ 30 = 2 units/day So, efficiency of 'B' = 3 X 2 = 6 units/day And efficiency of 'C' = 6 ÷ 2 = 3 units/day Let the number of days for which 'B' worked alone be 'd'. So, (d X 6) + (11 - d) X (2 + 3) = 60 Or, 6d + 55 - 5d = 60 Or, 'd' = 5 So, 'B' worked alone for 5 days So, 'B' should've joined them after (11 - 5) = 6 days
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