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# Some of 50%-intensity red paint is replaced with 25%

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Director
Joined: 09 Aug 2006
Posts: 515
Some of 50%-intensity red paint is replaced with 25%  [#permalink]

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17 Nov 2007, 08:05
3
22
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:20) correct 34% (01:03) wrong based on 548 sessions

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Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?

A. 1/30
B. 1/5
C. 2/3
D. 3/4
E. 4/5
Director
Joined: 01 Apr 2008
Posts: 821
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: PS : intensity red paint  [#permalink]

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24 Mar 2009, 22:37
13
4
Guys, I just happened to visit this link for mixture problems, and it really makes life easy:
http://www.onlinemathlearning.com/mixture-problems.html

They explained 3 different scenarios with mixtures: add, replace and mix. If you set up a table it becomes very easy.
For this problem

Concent 0.5 0.5 0.25 0.30
Amt 1 x x 1

So, orig - rem + add = result
(0.5) - 0.5 x + 0.25x = 0.30
0.5 - 0.25x = 0.30
0.25x = 0.20
x=4/5

Hope it helps:)
##### General Discussion
VP
Joined: 08 Jun 2005
Posts: 1139

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17 Nov 2007, 08:33
3
4
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint).

Attachments

MixtureI.JPG [ 6.53 KiB | Viewed 11949 times ]

Director
Joined: 26 Feb 2006
Posts: 882
Re: PS : intensity red paint  [#permalink]

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17 Nov 2007, 10:01
2
4
Amit05 wrote:
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?

* 1/30
* 1/5
* 2/3
* 3/4
* 4/5

Could anyone please explain me the wordings of this problem .. I have never heard the intensity of paint ..

forming an equation is always useful:

suppose, the total of 25% sol and 50% sol = 1
25% solution of red paint = x
50%-intensity red paint = 1-x

0.25 x + 0.5 (1-x) = 0.3
x = 4/5
Director
Joined: 09 Aug 2006
Posts: 745
Re: PS : intensity red paint  [#permalink]

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17 Nov 2007, 10:31
3
Amit05 wrote:
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?

* 1/30
* 1/5
* 2/3
* 3/4
* 4/5

Could anyone please explain me the wordings of this problem .. I have never heard the intensity of paint ..

Let total paint = 1
Let amount replaced = x

50 (1-x) + 25x = 30
x = 4/5
Director
Joined: 09 Aug 2006
Posts: 745

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17 Nov 2007, 10:35
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint). ---> how??

KS, I initially used the same diagram as you to solve the problem (I learned it a document attached to one of the posts). I determined that the new ratio is 1:4 but didn't know how to find out what fraction was replaced. I still don't understand how to figure that out after reading your post. Can you please explain? Thanks a bunch.
VP
Joined: 08 Jun 2005
Posts: 1139

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17 Nov 2007, 10:46
1
GK_Gmat wrote:
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint). ---> how??

KS, I initially used the same diagram as you to solve the problem (I learned it a document attached to one of the posts). I determined that the new ratio is 1:4 but didn't know how to find out what fraction was replaced. I still don't understand how to figure that out after reading your post. Can you please explain? Thanks a bunch.

Since you started only with the 50% paint (lets assume 10 liter) and you ended with 2 liter of that paint (2/10 = 1/5) then you replaced 8/10 = 4/5 of that paint. This takes some time to get used to - but once you get the hang of it you will solve it every time (or get your money back !).

Director
Joined: 09 Aug 2006
Posts: 745

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18 Nov 2007, 00:59
KillerSquirrel wrote:
GK_Gmat wrote:
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint). ---> how??

KS, I initially used the same diagram as you to solve the problem (I learned it a document attached to one of the posts). I determined that the new ratio is 1:4 but didn't know how to find out what fraction was replaced. I still don't understand how to figure that out after reading your post. Can you please explain? Thanks a bunch.

Since you started only with the 50% paint (lets assume 10 liter) and you ended with 2 liter of that paint (2/10 = 1/5) then you replaced 8/10 = 4/5 of that paint. This takes some time to get used to - but once you get the hang of it you will solve it every time (or get your money back !).

KS, I hate to be a pest but I couldn't get my head around this. How did you get 2 liter? Also, didn't we start with a ratio of 2:1 (50%:25%)? As you can tell, I'm totally confused. Thanks for any explanation in advance.
Director
Joined: 09 Aug 2006
Posts: 515

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18 Nov 2007, 03:58
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint).

So if I reiterate the question, can I say that some part of 50% solution was replaced by 25% solution and the resultant was 30 % solution ?
VP
Joined: 08 Jun 2005
Posts: 1139

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18 Nov 2007, 10:12
3
2
GK_Gmat wrote:
KillerSquirrel wrote:
GK_Gmat wrote:
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint). ---> how??

KS, I initially used the same diagram as you to solve the problem (I learned it a document attached to one of the posts). I determined that the new ratio is 1:4 but didn't know how to find out what fraction was replaced. I still don't understand how to figure that out after reading your post. Can you please explain? Thanks a bunch.

Since you started only with the 50% paint (lets assume 10 liter) and you ended with 2 liter of that paint (2/10 = 1/5) then you replaced 8/10 = 4/5 of that paint. This takes some time to get used to - but once you get the hang of it you will solve it every time (or get your money back !).

KS, I hate to be a pest but I couldn't get my head around this. How did you get 2 liter? Also, didn't we start with a ratio of 2:1 (50%:25%)? As you can tell, I'm totally confused. Thanks for any explanation in advance.

The question starts with a statement that you have a cerain amount of paint in 50% concentration (only 50% concentration and none from 25% concentration).

Using my diagram I found the new ratio of 50% to 25% to be 1:4.

Is this answer the question what fraction of the original paint was replaced ? Yes it does ! since you started with only 50% paint (i.e 5/5) and were left with 1/5 from this paint - meaning 4/5 was replaced.

And if you want to see it in numbers then assume we started with 10 liter of 50% paint or 20 liter for that matter, and the new ratio will give you 2:8 paint or 4:16 depending. So the amount that was replaced is 8/10 = 4/5 or 16/20 = 4/5

Attachments

Mixture Problems Made Easy.pdf [49.94 KiB]

Retired Moderator
Joined: 18 Jul 2008
Posts: 893
Re: PS : intensity red paint  [#permalink]

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24 Mar 2009, 15:32
the attached pdf is a really good document, but I think the explanations can be done a little bit better as I still had trouble wrapping my head around some of the methods.

Anyone care to give a look and try?
Manager
Joined: 17 Aug 2009
Posts: 202
Re: PS : intensity red paint  [#permalink]

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17 Nov 2009, 22:35
1
Let there be x litres of 50% solution initially
Suppose y litres of 50% solution is removed

Then the remaining solution is (x-y).50
Now, equal amount of solution that is replaced(y) is added, therefore => .25y

(x-y).50 + .25y = .30x
.20x = .25y
y=4/5

Hope this helps

Consider kudos for the post
Manager
Joined: 12 Jun 2007
Posts: 110
Re: PS : intensity red paint  [#permalink]

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16 Jul 2010, 02:18

Let the fraction be 3/4 and total capacity be 40 liter:

Fraction removed = 30 lts

originally intensity is 50% i.e. paint=20 lts and other =20 lts
now from this 30lt is removed so remaining will be, paint=5 lts and other=5 lts
now solution with 25% added (of 30lt) new solution will be, paint = 5 + 7.5 = 12.5 lts
Other = 5 + 22.5 = 27.5
now the ratio will be 12.5 / 40 = 33.75 and not equal to 30%, wrong answer

Let the fraction be 4/5 and total capacity be 100 liter:

Fraction removed = 80 lts

originally intensity is 50% i.e. paint=50 lts and other =50 lts
now from this 80lt is removed so remaining will be, paint=10 lts and other=10 lts
now solution with 25% added (of 80lt) new solution will be, paint = 10 + 20 = 30 lts
Other = 10 + 60 = 70 litre
now the ratio will be 30/100 = 30%, so this means this is the right choice
Retired Moderator
Joined: 16 Nov 2010
Posts: 1458
Location: United States (IN)
Concentration: Strategy, Technology
Re: PS : intensity red paint  [#permalink]

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14 Apr 2011, 19:08
1
1
Let original solution be 100 ml

and x ml of 25% solution be added to it

so 0.30(100) = 0.25x + 0.50(100 - x)

30 = 0.25x + 50 - 0.50x

=> 0.25x = 20

=> x = 80

So 80/100 = 4/5

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Manager
Joined: 23 Oct 2011
Posts: 82

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24 Oct 2011, 14:17
KillerSquirrel wrote:
See attachment

Intensity = concentration

since the new ratio is 5:20 = 1:4 then 4/5 was replaced (the old ratio was 1:0 ---> only 50% paint).

KillerSquirre, I would like to thank you for your great contribution (attachment with mixture problems) that makes mixture problems way easier to handle.

I have a question though, what does the 1:0 ratio mean?
Manager
Joined: 18 Jun 2010
Posts: 101
Re: PS : intensity red paint  [#permalink]

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24 Oct 2011, 21:00
+1 for E

25x+50(1-x) = 30

x=4/5
Manager
Joined: 23 May 2013
Posts: 112
Re: PS : intensity red paint  [#permalink]

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18 Oct 2013, 21:28
the attached pdf is a really good document, but I think the explanations can be done a little bit better as I still had trouble wrapping my head around some of the methods.

Anyone care to give a look and try?

Will try to elaborate on the PDF file,

Problem 3 on page 2

Assume we all understand how ratio of (x-16)/6 is achieved through rule of allegation. I struggled in understanding how that equal 3/1. Below is the explaination that i could come up.

Assume that initial quantity of solution = 10 litres
Problems states that 1/4 of the sol is removed --> implies that 2.5 litre of solution is removed; and replaced with solution of X % of sugar.
So the remaining fraction of original is 7.5 litres and the volume of new sol with x% of sugar = 2.5 litres
Hence (x-16)/6 = 3/1
Solving it we X = 34.

Last problem on page 4

We know that initial conc of acid was 50% and the final was 40%. Also by rule of allegation, each solution of acid was mixed in equal proportion. Hence in the final solution that we had, both 50% solution and 30% solution were in equal proportion. Assume that initially we had 1 litre of 50% solution, then we need to remove 500ml of 50% and replace it with 40% of 500 ml solution. Then the final will be 30%. Hence 1/2 of 50% solution was removed.

Hope it helps
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SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance
Re: Some of 50%-intensity red paint is replaced with 25%  [#permalink]

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16 Dec 2013, 06:05
1
Amit05 wrote:
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?

A. 1/30
B. 1/5
C. 2/3
D. 3/4
E. 4/5

Use smart numbers

Give 100 for the total of the original paint
So intensity paint is 50

Then you'll have 50-0.25x = 30
x = 80

So the ratio is 80/100 = 4/5

Hope it helps
Cheers!
J
Director
Joined: 23 Jan 2013
Posts: 598
Schools: Cambridge'16
Re: Some of 50%-intensity red paint is replaced with 25%  [#permalink]

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08 Nov 2015, 06:05
Equation

1/2x+1/4y=3/10(x+y)

x/y=1/4

Differential approach

50------30---25

20x=5y

x/y=1/4

x=1/5 and y=4/5 of final solution

E
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Re: Some of 50%-intensity red paint is replaced with 25%  [#permalink]

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09 Nov 2015, 03:15
The ratio for the 50% solution is 1:1, for the 25% is 1;3 and for the 30% mixture is 3;7

I just do the weighted average to find the weight of the 50% solution in the new 30% solution

$$\frac{x}{2}$$+$$\frac{1(1-x)}{4}$$=$$\frac{3}{10}$$

x = $$\frac{1}{5}$$

So $$\frac{4}{5}$$of the old 50% solution was replaced by 4/5 of the 25% solution

we get 0.2*50 + 0.8*25 = 30
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Re: Some of 50%-intensity red paint is replaced with 25% &nbs [#permalink] 09 Nov 2015, 03:15

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