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# Sam and David agreed to complete a work in 14 days.

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Manager
Joined: 20 Feb 2017
Posts: 56
Sam and David agreed to complete a work in 14 days. [#permalink]

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18 Nov 2017, 23:57
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65% (hard)

Question Stats:

61% (02:45) correct 39% (03:06) wrong based on 61 sessions

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Sam and David agreed to complete a work in 14 days. They also agreed to forfeit thrice the amount of wages corresponding to the unfinished if they failed to complete the work in 14 days. As they could not complete the work in 14 days, they lost 3/8th of the amount that they would have together received had they completed the work in time. If Sam alone can complete the work in 80 days,the time that David alone would take to complete the work is

A. 20 days
B. 24 days
C. 30 days
D. 35 days
E. 40 days

[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5732
Sam and David agreed to complete a work in 14 days. [#permalink]

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19 Nov 2017, 00:18
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Raksat wrote:
Sam and David agreed to complete a work in 14 days. They also agreed to forfeit thrice the amount of wages corresponding to the unfinished if they failed to complete the work in 14 days. As they could not complete the work in 14 days, they lost 3/8th of the amount that they would have together received had they completed the work in time. If Sam alone can complete the work in 80 days,the time that David alone would take to complete the work is

A. 20 days
B. 24 days
C. 30 days
D. 35 days
E. 40 days

hi...

you would see such Q more frequently in CAT

but let's solve it.

they were to lose thrice the amount of wages of work that was left ....
so if they lost $$\frac{3}{8}$$ of work, they did not do $$\frac{3}{8} * \frac{1}{3} = \frac{1}{8}$$ of work

In other words they did only $$1-\frac{1}{8} = \frac{7}{8}$$ of work
if they do 7/8 of work in 14 days, they will do complete job in 14*8/7 = 16 days..

David's one day work = $$\frac{1}{16}-\frac{1}{80} = \frac{5-1}{80}=\frac{4}{80}=\frac{1}{20}$$
so david does it in 20 days

A
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Joined: 20 Feb 2017
Posts: 56
Re: Sam and David agreed to complete a work in 14 days. [#permalink]

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19 Nov 2017, 00:23
chetan2u wrote:
Raksat wrote:
Sam and David agreed to complete a work in 14 days. They also agreed to forfeit thrice the amount of wages corresponding to the unfinished if they failed to complete the work in 14 days. As they could not complete the work in 14 days, they lost 3/8th of the amount that they would have together received had they completed the work in time. If Sam alone can complete the work in 80 days,the time that David alone would take to complete the work is

A. 20 days
B. 24 days
C. 30 days
D. 35 days
E. 40 days

hi...

you would see such Q more frequently in CAT

but let's solve it.

they were to lose thrice the amount of wages of work that was left ....
so if they lost $$\frac{3}{8}$$ of work, they did not do $$\frac{3}{8} * \frac{1}{3} = \frac{1}{8}$$ of work

In other words they did only $$1-\frac{1}{8} = \frac{7}{8}$$ of work
if they do 7/8 of work in 14 days, they will do complete job in 14*8/7 = 16 days..

David's one day work = $$\frac{1}{16}-\frac{1}{80} = \frac{5-1}{80}=\frac{4}{80}=\frac{1}{20}$$
so david does it in 20 days

A

Is there any method apart from UNITARY METHOD. Normally i take LCM and try to solve but some questions couldn't be solved using this method. And i couldn't grasp unitary method completely. Upto 700 level questions its fine but beyond 700 , it becomes a strech.
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2155
Re: Sam and David agreed to complete a work in 14 days. [#permalink]

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22 Nov 2017, 13:20
Raksat wrote:
Sam and David agreed to complete a work in 14 days. They also agreed to forfeit thrice the amount of wages corresponding to the unfinished if they failed to complete the work in 14 days. As they could not complete the work in 14 days, they lost 3/8th of the amount that they would have together received had they completed the work in time. If Sam alone can complete the work in 80 days,the time that David alone would take to complete the work is

A. 20 days
B. 24 days
C. 30 days
D. 35 days
E. 40 days

Since they lost 3/8 of the amount that they would have together received had they completed the job on time and they actually forfeited thrice the amount of wages corresponding to the unfinished, we can relate these two quantities as: ⅜ = 3x, and so x = ⅛, which means that they only had 1/8 of the job unfinished. In other words, they finished 7/8 of the job.

We can let n = the number of days David would take to complete the work alone. We are given that Sam would take 80 days to complete the work alone; thus, his rate would be 1/80, and David’s rate would be 1/n. Since they both worked 14 days, and they finished 7/8 of the job, we can create the following equation:

14 x 1/80 + 14 x 1/n = 7/8

14/80 + 14/n = 7/8

Multiply the equation by 80n we have:

14n + 1120 = 70n

1120 = 56n

n = 1120/56 = 20

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Re: Sam and David agreed to complete a work in 14 days. [#permalink]

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23 Feb 2018, 10:48
chetan2u wrote:
Raksat wrote:
Sam and David agreed to complete a work in 14 days. They also agreed to forfeit thrice the amount of wages corresponding to the unfinished if they failed to complete the work in 14 days. As they could not complete the work in 14 days, they lost 3/8th of the amount that they would have together received had they completed the work in time. If Sam alone can complete the work in 80 days,the time that David alone would take to complete the work is

A. 20 days
B. 24 days
C. 30 days
D. 35 days
E. 40 days

hi...

you would see such Q more frequently in CAT

but let's solve it.

they were to lose thrice the amount of wages of work that was left ....
so if they lost $$\frac{3}{8}$$ of work, they did not do $$\frac{3}{8} * \frac{1}{3} = \frac{1}{8}$$ of work

In other words they did only $$1-\frac{1}{8} = \frac{7}{8}$$ of work
if they do 7/8 of work in 14 days, they will do complete job in 14*8/7 = 16 days..

David's one day work = $$\frac{1}{16}-\frac{1}{80} = \frac{5-1}{80}=\frac{4}{80}=\frac{1}{20}$$
so david does it in 20 days

A

Hi chetan2u, CAT - are you referring to IIM CAT exams?

Thanks
Re: Sam and David agreed to complete a work in 14 days.   [#permalink] 23 Feb 2018, 10:48
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