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Work Rate

by yellowho » Sun Mar 06, 2011 1:28 am
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?
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by Night reader » Sun Mar 06, 2011 2:11 am
Work=w, Time=t --> (2/10)w=(8/10)t, (8/10)w=(2/10)t; t=30 days, w=X lines, last two weeks (1 week is seven days) = (7*2)/30=(7/15)t; The work completed in time --> t-(7/15)t= (8/15)t. This is less than (8/10)t, therefore [8/10 -8/15= 8/30]t there will be completed equivalent 2/10 portion of work (X) --> w=4t OR X=4t, (8/30)t means (2/10)*w/3 OR 2w/30 OR 2X/30=X/15 this much work has been completed. Uncompleted part of work is X-X/15=14X/15

recalculated
yellowho wrote: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?
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by Anurag@Gurome » Sun Mar 06, 2011 3:26 am
yellowho wrote: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?
80% of 30 days = 24 days and 20% of 30 days = 6 days
20% of X lines = (0.2)X lines and 80% of X lines = (0.8)X lines

We have to find how much did he wrote in last two weeks, i.e. last 14 days.

Now, in first 24 days, he wrote (0.2)X lines.

Hence, in first 16 days of the first 24 days, he wrote 16*(0.2)X/24 = (0.4)X/3 = 4X/30 = 2X/15 lines

Hence, in last 14 days, he wrote [X - 2X/15] = 13X/15 lines of code

Therefore, in last two weeks he wrote 13X/15 lines of code.
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by vineeshp » Sun Mar 06, 2011 3:41 am
I took the work done to be X.

Work done in the first 80% of 30 days, ie 24 days, is 0.2 X.
So work done in 1 day is 0.2/24 --> in 16 days is (.2/24) * 16

--> (4/30) X

so remaining work = X - (4/30)X = (26/30) X.
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by Night reader » Sun Mar 06, 2011 3:58 am
i made miscalc below, should have transversed to work after (8/30)t
@vin your answer is identical to Anurag's with reductions by 2 in nom/denom
Night reader wrote:Work=w, Time=t --> (2/10)w=(8/10)t, (8/10)w=(2/10)t; t=30 days, w=X lines, last two weeks (1 week is seven days) = (7*2)/30=(7/15)t; The work completed in time --> t-(7/15)t= (8/15)t. This is less than (8/10)t, therefore [8/10 -8/15= 8/30]t there will be completed equivalent 2/10 portion of work (X) --> w=4t OR X=4t, (8/30)t means (2/10)*w/3 OR 2w/30 OR 2X/30=X/15 this much work has been completed. Uncompleted part of work is X-X/15=14X/15

recalculated
yellowho wrote: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?
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by GMATGuruNY » Sun Mar 06, 2011 4:05 am
yellowho wrote: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?
We can plug in our own value for X.

Let X = 120 lines.
20% of the work = .2X = 24 lines.
80% of the time = 24 days.
Rate for first 24 days = w/t = 24/24 = 1 line per day.
Work completed in last 6 days = 120-24 = 96 lines.
Work completed in previous 8 days = r*t = 1*8 = 8 lines.
Total work completed in last 14 days = 96+8 = 104 lines. This is our target.

Now we plug X = 120 into all the answer choices to see which yields our target of 104.
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by gmatmachoman » Wed Mar 09, 2011 2:59 am
30 days can be written as = 8+8+8+6 days

we need last 2 weeks (14 days) = 8+6

24 days ------> 0.2X; so for 8 days X/15 days

From stem we know that 0.8X work is done in last 6 days

X/15 (accounting for 8 days) + 4X/5( accounting for 6 days)

= 13X/15
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