Vincen wrote:John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
A) 6
B) 10
C) 8
D) 7.5
E) 3.5
Let the job = the LCM of 20 and 12 = 60 units.
Since John can complete the job in 20 days, John's rate = w/t - 60/20 = 3 units per day.
Since Jane can complete the job in 12 days, Jane's rate = w/t = 60/12 = 5 units per day.
After Jane leaves, John works on his own for 4 days to complete the job.
Work produced by John in the last 4 days = r*t = 3*4 = 12 units.
Of the 60 units that must be produced, John produces the last 12.
Thus, the first 48 units are produced by John and Jane together.
Combined rate for John and Jane = 3+5 = 8 units per day.
Time for John and Jane to produce 48 units = w/r = 48/8 = 6 days.
Total time for the job = (4 days for John alone) + (6 days for John and Jane together) = 10 days.
The correct answer is
B.
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