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

Question

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

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

blueseas · Answer

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

Asifpirlo · Answer

...
in 24 liters, Red = 5/8 * 24 = 15 and Blue = 9
so, 15/(9+x) = 3/5 
or, x = 16 (Answer D)

intheend14 · Answer

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

PareshGmat · Answer

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

law258 · Answer

Set up the equation as follows:

x + 24(3/8) = (24+x)(5/8)
3x=48
x=16

yezz · Answer

(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)

D

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

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