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

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

02 Feb 2010, 06:30

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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

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Re: Ratio of Time to complete task [#permalink]

02 Feb 2010, 07:21

Yes. Can u pl explain the working?

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Re: Ratio of Time to complete task [#permalink]

02 Feb 2010, 09:32

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answer is B:

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

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Re: Ratio of Time to complete task [#permalink]

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

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Re: If Dev works alone he will take 20 more hours to complete a [#permalink]

18 Jan 2013, 23:08

jusjmkol740 wrote:

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

Re: If Dev works alone he will take 20 more hours to complete a [#permalink] 18 Jan 2013, 23:08

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

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

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