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A software programmer does 20% of the work in 80% of the

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A software programmer does 20% of the work in 80% of the  [#permalink]

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New post 01 Dec 2012, 02:58
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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?

1) 13x/15
2) 7x/15
3) 7x/60
4) 2x/3
5) x/2

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Re: Work Problem - Need help on this.  [#permalink]

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New post 01 Dec 2012, 03:55
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manukumar 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?

1) 13x/15
2) 7x/15
3) 7x/60
4) 2x/3
5) x/2


Pick nos. Take x = 60
1st stage -> 20% of the work in 80% of the time
So 20% of 60 = 12
and 80% of 30 (nos of days) = 24
So he writes 12 lines of code in 1st 24 days

2nd stage -> 80% of the work in the remaining 20% of the time
so he writes 48 lines of code in last 6 days.

The 2 boldface are your rates.
In the last 14 days comprises of both the stages.
in the 1st 8 days he writes at the rate of\(\frac{12}{24} \frac{lines}{days}\) so he writes 4 lines ( \(8 * \frac{12}{24}\))
in the last 6 days he writes at the rate of\(\frac{48}{6}\) lines / days so he writes 48 lines (\(6 *\frac{48}{6}\))

totally he writes 52 lines. This is the final value / target value.
Substitute X = 60 and check which one results in 52.

Only option A gives 52 when x = 60.

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Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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New post 22 Aug 2014, 06:08
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1
Total work - x lines
Total time - 30 days

20% work done in 80% time... given
20% of work= x/5
80% of time=30*0.8=24 days
Therefore rate for first 24 days=(x/5)/24=x/120

We have been asked to compute work completed in last 2 weeks, i.e. last 14 days
Work done in last 14 days=Total work-work done in first 16 days
= x-[(x/120)*16]
= x-(2x/15)
= 13x/15
Ans= A
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A software programmer does 20% of the work in 80% of the  [#permalink]

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New post 25 Aug 2014, 10:56
This question can be answered without any computation.
As the 80% of work is done in the last 6 days( 20% of 30 days). Then the work done in the last 14 days must be more than 80% i.e. 4/5 (For the possible answer the numerator must be greater than half of the denimenator) and there are two possible options A (13x/15 ) and D (2x/3 ) Clearly D is just 66.67% and the obvious choice is answer choice A.

Or, if we want to kill some time and do the tedious job of computing, we can do the same as follows :
For first part, the time spent is is 80% of 30 days = 30*0.8 =24 days ( Here the programmer does 20% of the work (x) i.e. 1x/5)

For the second part, the time spent is 20% of 30 days= 30*0.2= 6 days ( Here the programmer does 80% of work (x) i.e. 4x/5)

Now lets see, what part of work the programmer does in last 14 days.

Last 14 days= 8 days + 6 days (last 6 days)
= [(1x/5)*(1/24)]*8 + 4x/5
=1x/15 +4x/5
=13x/15
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Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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New post 03 Sep 2015, 11:51
1
Here is the pictorial representation of the situation:


Work = X Time = 30 days Last 15 days work
1) 20% = 1/5X 80% = 24 days 8 days of work = 24 days of work/3 = 1/3*1/5x = 1/15*x
2) 80% = 4/5X 20% = 6 days 6 days of work = 4/5*x

Last 15 days will be 8 days from the 1) and 6 days from 2) = (4/5+1/15)*x = 13/15*x
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Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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Re: A software programmer does 20% of the work in 80% of the &nbs [#permalink] 01 Feb 2018, 00:36
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