Question

Nein is preparing two cans of paint for a client. The first is $60$ parts blue paints and $25$ parts red paint ; the second is $70$ parts blue paint, $30$ parts yellow paint, and $15$ parts white paint. The client asked to prepare another can using only white and red paint as per the ratio in the first and second can. Determine the ratio of white and red paint that Nein would use in the third can.

• A. 35:18
• B. 18:35
• C. 5:3
• D. 3:5

Answer 1

Answer: (B)

18:35

The first paint can has a red:blue $(R:B)$ ratio of $25:60$

The second can's ratio, yellow:blue:white $(Y:B:W)$, is $30:70:15$.

Reduce the ratios to make the math easier.

$R:B$ becomes $5:12$, and $Y:B:W$ becomes $6:14:3$.

These cannot be combined as they are, so you need a common factor to link them. Blue is the term common to both ratios.

Look for a small common multiple of the blue components, $12$ and $14$.

Using $84$ as the common multiple, determine factors that, when multiplied by the ratios.

Turn both blue components into $84$.

For $R:B$, the calculation is $7\times (5:12)=35:84$

Repeating for $Y:B:W$, you get $6\times (6:14:3)=36:84:18$

The combined ratio $R:B:Y:W$ becomes $35:84:36:18$, making $R:W35:18$.

The question asks for the ratio of white to red, so flip your ratio to get $18:35$, which is (B)