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Suzanne and Melody can paint home in 10 and 15 days respecti

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Suzanne and Melody can paint home in 10 and 15 days respecti [#permalink]

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Suzanne and Melody can paint home in 10 and 15 days respectively. They started painting but unfortunately Suzanne has to leave after some days and Melody finished remaining task in 5 days. After how many days did Suzanne left?

A. 10
B. 4
C. 5
D. 20
E. 6
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Feb 2013, 03:14, edited 1 time in total.
Renamed the topic.

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Re: Suzanne and Melody can paint home [#permalink]

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New post 17 Feb 2013, 04:28
Amount of the work done by Suzanne and Melody in one day = [1/10 + 1/15] of the work

Let x be the number of days that Suzanne and Melody worked together on the project (before Suzanne left)
Amount of the total work done in this time = x [1/10 + 1/15] of the work
After this, Melody worked for 5 days more.
Amount of the total work done by Melody in this time = 5[1/15] = 1/3rd of the work

As Melody finished 1/3rd of the work in the remaining 5 days, we can infer that together Suzanne and Melody finished 2/3rd of the work in x days
=> x[1/10 + 1/15] = 2/3
=> x = 4 days

The answer is choice (B)
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Re: Suzanne and Melody can paint home [#permalink]

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New post 17 Feb 2013, 06:44
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Total Work = 100%
Suzanne can paint home in 10 days. So in one day she can paint 10% of home
Melody can paint home in 15 days. So in one day she can paint 6.66% of home
In one day together they can paint 16.66% of home.

They together worked for some days.

Later Suzanne left and melody had to complete remaining task in 5 days. In those 5 days she must have completed 6.66 X 5 = 33.30 % of job

So together they must have completed 100-33.30 = 66.70% job. in one day they can finish 16.66% of job. so they worked together for (66.70/16.66) = 4 days.

That means suzanne worked for 4 days and then left.

Regards,

Abhijit.
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Re: Suzanne and Melody can paint home in 10 and 15 days respecti [#permalink]

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New post 18 Feb 2013, 03:22
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antoxavier wrote:
Suzanne and Melody can paint home in 10 and 15 days respectively. They started painting but unfortunately Suzanne has to leave after some days and Melody finished remaining task in 5 days. After how many days did Suzanne left?

A. 10
B. 4
C. 5
D. 20
E. 6


In 5 days that Melody worked alone she completed 5/15=1/3 of the work, thus Suzanne and Melody when working together completed 2/3 of the work.

Since their combined rate is 1/10+1/15=1/6 work/day, then they worked for (time)=(job)/(rate)=(2/3)/(1/6)=4 days.

Answer: B.

Hope it's clear.
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Re: Suzanne and Melody can paint home in 10 and 15 days respecti [#permalink]

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New post 25 Sep 2016, 08:38
antoxavier wrote:
Suzanne and Melody can paint home in 10 and 15 days respectively. They started painting but unfortunately Suzanne has to leave after some days and Melody finished remaining task in 5 days. After how many days did Suzanne left?

A. 10
B. 4
C. 5
D. 20
E. 6


Let the total work be 30 Units..

So, Suzanne's efficiency = 3 units/day
and , Melody 's efficiency = 2 units/day

Let the take d days to complete the job...

5*2 + d ( 3 + 2 ) = 30

10 + 5d = 30

Or, 5d = 20

Or, d = 4

So , Answer will be (B) 4 days..
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Re: Suzanne and Melody can paint home in 10 and 15 days respecti [#permalink]

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New post 26 Nov 2017, 04:38
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Suzanne and Melody can paint home in 10 and 15 days respecti   [#permalink] 26 Nov 2017, 04:38
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