Question
Amit', 'Bhanu', and 'Chintu' can finish a piece of work
in 51 days, 85 days, and 102 days respectively. They all begin working together on the task, but 'Bhanu' stops working 19 days before the work is completed, and 'Amit' leaves 9 days before it ends. Determine the total number of days required to complete the work.Solution
ATQ,
Let the total work be 510 units (LCM of 51, 85 and 102)
Efficiency of 'Aman' = (510/51) = 10 units/day
Efficiency of 'Bhanu' = (510/85) = 6 units/day
Efficiency of 'Chintu' = (510/102) = 5 units/day
Let the time taken to complete the work be 'd' days.
So, (10 + 6 + 5) X (d - 19) + (10 + 5) X 10 + 5 X 9 = 510
Or, 21d - 399 + 150 + 45 = 510
Or, 21d = 714
Or, 'd' = 34
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