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At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red

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At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 10 Aug 2013, 01:57
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At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?

A) 9
B) 12
C) 15
D) 16
E) 18
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 10 Aug 2013, 02:13
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aparnaharish wrote:
At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue
paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many
liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?

A) 9
B) 12
C) 15
D) 16
E) 18


to conver F paint to M paint ratio of red/ratio of blue = \(\frac{3}{5}\) (as this is the ratio in M paint)

let F has \(5a\) litre red paint and \(3a\) litre blue paint==>\(8a=24\) ==>\(red =15\) and\(blue =9\)
let \(x\) LITRES blue paint is addded .
total blue paint = \(9 + x\)
now ratio = \(\frac{15}{(9+x)}\) this must be equal to \(\frac{3}{5}\)
now on solving ==> \(75=27+3x\)==>\(x=16\)

hence D
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 10 Aug 2013, 03:54
1
1
aparnaharish wrote:
At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue
paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many
liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?

A) 9
B) 12
C) 15
D) 16
E) 18

...
in 24 liters, Red = 5/8 * 24 = 15 and Blue = 9
so, 15/(9+x) = 3/5
or, x = 16 (Answer D)
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 02 Dec 2014, 08:37
I'll abbreviate all colors with their first initial to simply things: f (Fuchsia), m (Mauve), r (Red) and b (Blue).
f requires 5L red to 3L blue. In 24L of f, we have 15L red and 9L blue.
m requires 3L red to 5L blue. Since we currently have 15L red, we need a total of 25L of blue to get the 3:5 ratio in m.
For this, we need to add 16L of blue to f to get to m color paint.

Answer is D
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 02 Dec 2014, 20:12
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Answer = D) 16

Red ....................... Blue ................... Total

15 ............................ 9 ........................... 24 (Fuchsia Paint)

15 ........................... 9+x .......................... 24+x (Say Quantity x blue paint is added)

Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint

So, blue portion is Mauve paint \(= \frac{5}{8}\) & red portion \(= \frac{3}{8}\)

Setting up the equation (Results would be same; I prefer the first one)

\(\frac{15}{24+x} = \frac{3}{8}\)OR

\(\frac{9+x}{24+x} = \frac{5}{8}\)

x = 16
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 27 Oct 2016, 14:36
Set up the equation as follows:

x + 24(3/8) = (24+x)(5/8)
3x=48
x=16
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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 11 Nov 2016, 23:12
1
aparnaharish wrote:
At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?

A) 9
B) 12
C) 15
D) 16
E) 18



(5-3 = 2) (8-5=3)
3/8 ........................................................5/8..............................................................................................................8/8
( blue paint in fuchsia) (blue paint in mauve) (100% blue paint)


to obtain the mauve we have to mix fuchsia and pure blue in the ratio 3:2

to obtain move we need to mix 2 liters of blue for every 3 liters of fuchsia and since we have (8) 3-liters of fuchsia in 24 liters of fuchsia thus we need to add (8*2 = 16 of pure blue)

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Re: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red  [#permalink]

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New post 15 Dec 2017, 09:46
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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: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red &nbs [#permalink] 15 Dec 2017, 09:46
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At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red

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