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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 [#permalink] New post   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] New post   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: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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?
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)
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Re: Ratio of Time to complete task [#permalink] New post   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] New post   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
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   07 Nov 2017, 05:22
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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)
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   18 Mar 2014, 04:58
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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
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If Dev works alone he will take 20 more hours to complete a [#permalink] New post   Updated on: 07 Nov 2017, 09:35
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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

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.
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If Dev works alone he will take 20 more hours to complete a [#permalink] New post   Updated on: 23 Sep 2016, 11:39
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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.
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   01 Nov 2017, 17:11
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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


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
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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?
Experts please advice

Cheers
J
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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 :)
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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 ?
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   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!
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   25 Aug 2019, 10:34
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


Given:
1, If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task.
2. 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.

Asked: 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?

Let the time taken by Dev and Tina be d & t respectively

Q: d/t = ?

Time taken by Dev and Tina to complete the task = dt/(d+t)

1, If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task.

d - dt/(d+t) = 20 (1)

2. 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.

t - dt/(d+t) = 5 (2)

d - t = 15
d = t + 15. (3)

t - (t+15)t/(2t+15) = 5
2t^2 + 15t - t^2 - 15t = 10t + 75
t^2 -10t -75 =0
t^2 - 15 t + 5t - 75 =0
(t+5)(t-15) = 0
t = 15
d = t + 15 = 30

d/t = 30/15 = 2
d:t = 2:1

IMO B
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   13 Nov 2019, 22:18
Expert Reply
VeritasKarishma 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)


Quote:
Hi Karishma..could you please explain how did you get 20/t and t/5 below?. I am still very confused.


You can think about it in terms of ratio fo speeds.

Say Dev and Tina are working together and they take t hrs to complete the work (as per their speeds). Some part of work is done by Dev (as per his speed) and rest is done by Tina (as per her speed). That is how they both finish it in t hrs.

Now, when Dev works alone, he takes t hrs + another 20 hrs to finish the same work. Dev takes 20 hrs extra when working alone because Tina did not work for t hrs. So whatever work Tina was doing in t hrs, Dev did it in 20 hrs.
Ratio of time taken by Dev/Tina = 20/t
Ratio of speeds when work done is same is inverse of ratio of time taken.
Ratio of speeds of Dev/Tina = t/20

On the same lines, when Tina works alone, she takes 5 hrs extra.
Ratio of time taken by Dev/Tina = t/5
Ratio of speeds of Dev/Tina = 5/t

Since speeds of Dev and Tina are constant, this ratio will not change.

t/20 = 5/t
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If Dev works alone he will take 20 more hours to complete a [#permalink] New post   Updated on: 01 Jul 2020, 14:50
VeritasKarishma wrote:
VeritasKarishma 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)


Quote:
Hi Karishma..could you please explain how did you get 20/t and t/5 below?. I am still very confused.


You can think about it in terms of ratio fo speeds.

Say Dev and Tina are working together and they take t hrs to complete the work (as per their speeds). Some part of work is done by Dev (as per his speed) and rest is done by Tina (as per her speed). That is how they both finish it in t hrs.

Now, when Dev works alone, he takes t hrs + another 20 hrs to finish the same work. Dev takes 20 hrs extra when working alone because Tina did not work for t hrs. So whatever work Tina was doing in t hrs, Dev did it in 20 hrs.
Ratio of time taken by Dev/Tina = 20/t
Ratio of speeds when work done is same is inverse of ratio of time taken.
Ratio of speeds of Dev/Tina = t/20

On the same lines, when Tina works alone, she takes 5 hrs extra.
Ratio of time taken by Dev/Tina = t/5
Ratio of speeds of Dev/Tina = 5/t

Since speeds of Dev and Tina are constant, this ratio will not change.

t/20 = 5/t


Hi VeritasKarishma -- is there a Veritas blog post on this type of solving strategy specifically or on this concept ?

I need to solve more problems to inculcate this on D day (under 2 minute time pressure)

Any problems you can suggest with this strategy or where i can pick up some theory on this strategy ?

Originally posted by jabhatta2 on 01 Jul 2020, 10:39.
Last edited by jabhatta2 on 01 Jul 2020, 14:50, edited 1 time in total.
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink] New post   01 Jul 2020, 14:47
Probably not the best approach, but this is what i did

1 = 1/a(t+20) --->1/a = 1/(t+20)
1 = 1/b(t+5) -----> 1/b = 1/(t+5)

1 = (1/a+1/b)t
1 = [1/(t+20) + 1/(t+5)]t
1 = t/(t+20) + t/(t+5)
plugin some obvious values (i.e t=10
1 = 1/3+2/3 ---> confirmed t=10

20+10:5+10
30:15
2:1
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Re: If Dev works alone he will take 20 more hours to complete a [#permalink]
01 Jul 2020, 14:47
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