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# If Dev works alone he will take 20 more hours to complete a

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Manager
Joined: 25 Nov 2009
Posts: 57
Location: India
If Dev works alone he will take 20 more hours to complete a [#permalink]

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02 Feb 2010, 06:30
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75% (hard)

Question Stats:

62% (02:20) correct 38% (02:36) wrong based on 509 sessions

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If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2
Manager
Joined: 17 Jan 2010
Posts: 139
Concentration: General Management, Strategy
GPA: 3.78
WE: Engineering (Manufacturing)

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02 Feb 2010, 09:32
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If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?

Take the time necessary to complete the job by both Dev and Tina to be x.
From the problem statement, time necessary to complete the job by Dev alone is: x+20
From the problem statement, time necessary to complete the job by Tina alone is: x+5

Rate of work when Dev and Tina work together: 1/x
Rate of work when Dev works alone: 1/(20+x)
Rate of work when Tina works alone: 1/(5+x)

The rate of work when Tina and Dev works together is equal to sum of the rates when Tina and Dev work alone:

1/x=1/(20+x)+ 1/(5+x)
When simplified the equation becomes:

X^2=100

X can only be the positive as we talk about tome, so x=10

The necessary ratio is T(Dev)/T(Tina)=(x+20)/(x+5)=30/15=2:1
Intern
Joined: 16 May 2011
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01 May 2012, 07:46
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Let time taken by Dev to complete the work alone be x days and that by Tina be y days

Work done by Dev in 1 day = 1/x
Work done by Tina in 1 day = 1/y

Work done by Dev & Tina in 1 day = 1/x + 1/y = (x+y)/xy
Thus working together they will complete the work in xy/(x+y) days
Acc. to the ques :

1) "If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina'

x - xy/(x+y) = 20
=> (x^2)/(x+y) = 20.............(i)

2) "If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev"

y - xy/(x+y) = 5
=> (y^2)/(x+y) = 5..............(ii)

Dividing (i) by (ii)

x^2/y^2 = 4
=> x/y = 2

Ans : B
Hope it helps
Intern
Joined: 11 Feb 2012
Posts: 14
Re: If Dev works alone he will take 20 more hours to complete a [#permalink]

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18 Jan 2013, 23:08
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jusjmkol740 wrote:
If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2

Solved it in a minute! Here's my solution:

Description of the formula used:
If A and B complete a task in x days, then A alone takes=x+a days and B alone take x+b days
Formula: x=\sqrt{ab}

Plugging in the numbers:
x=\sqrt{20*5}
= 10

=>A=20+10=30 and B=5+10=15
=>a/b=2/1
Current Student
Joined: 06 Sep 2013
Posts: 1891
Concentration: Finance
Re: If Dev works alone he will take 20 more hours to complete a [#permalink]

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18 Feb 2014, 06:43
jusjmkol740 wrote:
If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2

Is there any way to solve this problem in a time efficient way?

Cheers
J
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India
Re: If Dev works alone he will take 20 more hours to complete a [#permalink]

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18 Feb 2014, 21:35
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jlgdr wrote:
jusjmkol740 wrote:
If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2

Is there any way to solve this problem in a time efficient way?

Cheers
J

Let's say when they work together, they take t hrs to complete the work.
Dev takes 20 hrs extra when working alone because Tina did not work for t hrs and that work Dev had to do. Ratio of time take by Dev/Tina to do the same work = 20/t
Tina takes 5 hrs extra when working alone because Dev did not work with her for t hrs and hence his part of work, Tine did in 5 hrs. Ratio of time taken by Dev/Tina to do the same work = t/5
20/t = t/5 (The ratio of time taken by Dev and Tina for the same work will always be the same irrespective of the amount of work)
t = 10
Ratio of time taken by Dev/Tina = 20:10 = 2:1
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 03 Aug 2012 Posts: 830 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 18 Mar 2014, 04:58 1 This post received KUDOS Again the funda of Rate * Time = Work Time (Both) = T For Dev: Rate (Both) =T Rate * Time = Work Rate * T+20 = 1 Rate (Dev) = 1/(T+20) For Tina: Rate * Time = Work Rate * T+5 = 1 Rate (Tina) = 1/(T+5) Combined Rates = 1/(T+20) + 1/(T+5) = 1/T Solving for it we will get you will get T=10 We want to know what is Time(D)/Time(T)= (T+20)/(T+5)=2:1 _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Director Joined: 23 Jan 2013 Posts: 596 Schools: Cambridge'16 Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 13 Sep 2015, 06:50 Guessing strategy says that it is B or E. Because guy works slower that girl, it must be B. Otherwise you can do algebra as written above B Director Joined: 07 Dec 2014 Posts: 999 If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags Updated on: 07 Nov 2017, 09:35 1 This post received KUDOS If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task? A. 4 : 1 B. 2 : 1 C. 10 : 1 D. 3 : 1 E. 1 : 2 let t=D and T's time working together ratio of D's time working alone to T's time working alone=(t+20)/(t+5) plugging in answer options, only 2:1 works (t+20)/(t+5)=2/1 t=10 t+20=30 t+5=15 30:15=2:1 B Originally posted by gracie on 30 Nov 2015, 16:02. Last edited by gracie on 07 Nov 2017, 09:35, edited 1 time in total. Board of Directors Joined: 17 Jul 2014 Posts: 2734 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags Updated on: 23 Sep 2016, 11:39 time work together: x time dev = x+20 time tina = x+5 1/x+20 + 1/x+5 = 1/x x+20+x+5/(x+20)(x+5) = 1/x 2x+25/(x+20)(x+5) = 1/x cross multiply 2x^2 +25x = x^2 +5x+20x + 100 rearrange: x^2 - 100 = 0 factor: (x+10)(x-10)=0 x=10 or x=-10, since we are talking about hours, -10 is not a solution, thus x=10. time for dev=10+20=30 time tina = 10+5=15 time dev/time tina = 30/15 = 2/1 Originally posted by mvictor on 13 Jan 2016, 19:16. Last edited by mvictor on 23 Sep 2016, 11:39, edited 1 time in total. Intern Joined: 10 Mar 2015 Posts: 10 Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 23 Sep 2016, 11:23 mvictor wrote: time work together: x time dev = x+20 time tina = x+5 1/x+20 + 1/x+5 = 1/x x+20+x+5/(x+20)(x+5) = 1/x 2x+25/(x+20)(x+5) = 1/x cross multiply 2x^2 +25x = x^2 +5x+25x-100 rearrange: x^2 - 100 = 0 factor: (x+10)(x-10)=0 x=10 or x=-10, since we are talking about hours, -10 is not a solution, thus x=10. time for dev=10+20=30 time tina = 10+5=15 time dev/time tina = 30/15 = 2/1 I think there is a typo. Should be 20x -100 Board of Directors Joined: 17 Jul 2014 Posts: 2734 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 23 Sep 2016, 11:28 Jargalan wrote: mvictor wrote: time work together: x time dev = x+20 time tina = x+5 1/x+20 + 1/x+5 = 1/x x+20+x+5/(x+20)(x+5) = 1/x 2x+25/(x+20)(x+5) = 1/x cross multiply 2x^2 +25x = x^2 +5x+25x-100 rearrange: x^2 - 100 = 0 factor: (x+10)(x-10)=0 x=10 or x=-10, since we are talking about hours, -10 is not a solution, thus x=10. time for dev=10+20=30 time tina = 10+5=15 time dev/time tina = 30/15 = 2/1 I think there is a typo. Should be 20x -100 where exactly? I don't see it Intern Joined: 10 Mar 2015 Posts: 10 Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 23 Sep 2016, 11:35 mvictor wrote: Jargalan wrote: mvictor wrote: time work together: x time dev = x+20 time tina = x+5 1/x+20 + 1/x+5 = 1/x x+20+x+5/(x+20)(x+5) = 1/x 2x+25/(x+20)(x+5) = 1/x cross multiply 2x^2 +25x = x^2 +5x+25x-100 rearrange: x^2 - 100 = 0 factor: (x+10)(x-10)=0 x=10 or x=-10, since we are talking about hours, -10 is not a solution, thus x=10. time for dev=10+20=30 time tina = 10+5=15 time dev/time tina = 30/15 = 2/1 I think there is a typo. Should be 20x -100 where exactly? I don't see it This: 2x^2 +25x = x^2 +5x+25x-100 shouldn't it be 2x^2 +25x = x^2 +5x +20x +100 ? Board of Directors Joined: 17 Jul 2014 Posts: 2734 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 23 Sep 2016, 11:39 Jargalan wrote: This: 2x^2 +25x = x^2 +5x+25x-100 shouldn't it be 2x^2 +25x = x^2 +5x +20x +100 ? yes, you are correct! nice catch! 2x^2 +25x = x^2 +5x+20x + 100 is the correct form i will have it edited now! Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2638 Location: United States (CA) Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 01 Nov 2017, 17:11 1 This post received KUDOS Expert's post jusjmkol740 wrote: If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task? A. 4 : 1 B. 2 : 1 C. 10 : 1 D. 3 : 1 E. 1 : 2 We can let x = the time it takes for Dev and Tina working together to complete the task. Thus, the time it takes Dev to work alone = x + 20 and the time it takes Tina to work alone = x + 5. Thus, their combined rate can be equated as follows: 1/(x + 20) + 1/(x + 5) = 1/x Let’s first get a common denominator of (x + 20)(x + 5) for the left side of the equation: [(x + 5) + (x + 20)]/[(x + 20)(x + 5)] = 1/x Combining like terms in the numerator on the left side of the equation yields: (2x + 25)/[(x + 20)(x + 5)] = 1/x Cross-multiplying, we obtain: x(2x + 25) = (x + 20)(x + 5) 2x^2 + 25x = x^2 + 25x + 100 x^2 = 100 x = 10 Since x = 10, the time it takes Dev to work alone = 10 + 20 = 30 and the time it takes Tina to work alone = 10 + 5 = 15. Thus, the ratio of the time taken by Dev to that taken by Tina if each worked alone is 30/15 = 2/1. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8079 Location: Pune, India Re: If Dev works alone he will take 20 more hours to complete a [#permalink] ### Show Tags 07 Nov 2017, 05:22 2 This post received KUDOS Expert's post VeritasPrepKarishma wrote: jlgdr wrote: jusjmkol740 wrote: If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task? A. 4 : 1 B. 2 : 1 C. 10 : 1 D. 3 : 1 E. 1 : 2 Is there any way to solve this problem in a time efficient way? Experts please advice Cheers J Let's say when they work together, they take t hrs to complete the work. Dev takes 20 hrs extra when working alone because Tina did not work for t hrs and that work Dev had to do. Ratio of time take by Dev/Tina to do the same work = 20/t Tina takes 5 hrs extra when working alone because Dev did not work with her for t hrs and hence his part of work, Tine did in 5 hrs. Ratio of time taken by Dev/Tina to do the same work = t/5 20/t = t/5 (The ratio of time taken by Dev and Tina for the same work will always be the same irrespective of the amount of work) t = 10 Ratio of time taken by Dev/Tina = 20:10 = 2:1 Answer (B) Responding to a pm: Quote: could you please explain how did you take 20/t and t/5 ? thanks in advance. If they both work together, say they take t hrs. So Dev is working for t hours and Tina is working for t hrs. They complete the work in this way. What happens when Dev works alone? He works for t hrs but Tina doesn't. So he works for another 20 hrs. Why? Because Tina did not work for t hrs. So whatever work Tina did in t hrs is now done by Dev in 20 hrs. So, time taken by Dev to do a certain work/Time taken by Tina to do the same work = 20/t Note that this is inverse of the ratio of their rates (since work done is the same) In exactly the same way Tina does Dev's work in 5 hrs so Time taken by Dev to do a certain work/Time taken by Tina to do the same work = t/5 Note that this too is inverse of the ratio of their rates (since work done is the same) Hence, 20/t = t/5 On solving this, you get answer (B) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If Dev works alone he will take 20 more hours to complete a   [#permalink] 07 Nov 2017, 05:22
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# If Dev works alone he will take 20 more hours to complete a

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