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In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture

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In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture

by Mikrislac » Sun Jul 26, 2020 1:47 am

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In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture was taken out and 4 litres of blue paint and 4 litres of yellow paint were added to the mixture. The ratio of blue paint to yellow paint in the new mixture became 8:3. What was the quantity of the mixture that was taken out initially?

A. 10 litres
B. 12 litres
C. 15 litres
D. 18 litres
E. 20 litres
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Re: In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture

by Mikrislac » Thu Jul 30, 2020 3:36 pm
The key to solving this problem is to recognize the following concept. If the ratio of blue paint (B) to yellow paint (Y) in the original mixture was 4:1, then the same ratio for the two paints will hold when a certain quantity of the mixture is taken out.

So, the ratio of Y to B in new mixture = 4:1. Assume x is the multiplier. Then, the quantities of Y and B in the new mixture are respectively, 4x and 1x. If we can determine the value of x, we can determine the quantities of the respective paints in the new mixture. The difference between the original quantity (40 litres) and the new total quantity (4x + 1x) will be the amount of the mixture that was taken out.

Four litres of each of B and Y were added to the new mixture. Hence, the new ratio will be (4x+4)/(x+4). This should be equal to 8:3 (given). Solving for x, we get x = 5 litres.

Therefore, the total quantity of the new mixture is equal to (4x+1x) or 25 litres. Since the original quantity of the mixture was 40 litres, the amount of the mixture that was taken out is equal to 40 - 25 = 15 litres.

Answer: C
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Re: In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture

by Scott@TargetTestPrep » Sun Aug 02, 2020 8:52 am
Mikrislac wrote: ↑
Sun Jul 26, 2020 1:47 am
 In a 40 litre mixture of paint, the ratio of blue paint to yellow paint was 4:1. A certain quantity of the mixture was taken out and 4 litres of blue paint and 4 litres of yellow paint were added to the mixture. The ratio of blue paint to yellow paint in the new mixture became 8:3. What was the quantity of the mixture that was taken out initially?

A. 10 litres
B. 12 litres
C. 15 litres
D. 18 litres
E. 20 litres
Solution:

We see that originally, 32 liters of the mixture is blue paint and 8 liters is yellow paint. We can let 5x liters be the quantity of the mixture that was taken out so that 4x liters of blue paint and x liters of yellow paint were taken out. We can create the equation:

(32 - 4x + 4) / (8 - x + 4) = 8/3

(36 - 4x)/(12 - x) = 8/3

3(36 - 4x) = 8(12 - x)

108 - 12x = 96 - 8x

12 = 4x

3 = x

Therefore, 5(3) = 15 liters of the mixture were taken out initially.

Answer: C

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