Let x = 120 lines.A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is x lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of x?
13x/15
7x/15
7x/60
2x/3
x/2
First stage:
20% of the work = 20% of 120 lines = 24 lines.
80% of the total time = 80% of 30 days = 24 days.
Since 20% of the work is completed in 80% of the total time, we get:
Rate = w/t = (24 lines)/(24 days) = 24/24 = 1 line per day.
Thus:
Since the rate is 1 line per day, the amount of work completed in the last 8 days of the first stage = rt = 1*8 = 8 lines.
Second stage:
Work completed in the last 6 days of the month = (total work) - (work completed in the first 24 days) = 120-24 = 96 lines.
Total work completed in last 14 days = 8+96 = 104 lines. This is our target.
Now plug x=120 into the answer choices to see which yields our target of 104.
Only A works:
13x/15 = (13*120)/15 = 13*8 = 104.
The correct answer is A.
