Question

To make green paint, a painter mixes yellow paint and blue paint in the ratio of 3 : 2. If he used twelve litres of yellow paint, how much blue paint did he use?

Answer 1

Hint: Assume the volume of yellow and blue paint mixed as $3x$ and $2x$ respectively. Equate this assumed volume of yellow paint with 12 and find the value of $x$. Now, equate this value of $x$ obtained in the assumed volume of blue paint and get the answer.

Complete step by step answer:
Here, we have been given that in the process of making green paint, the painter mixes yellow and blue paint in the ratio 3 : 2. Therefore, it can be assumed that,
Volume of yellow paint used = $3x$
Volume of blue paint used = $2x$
Now, it is given that the painter used 12 litres of yellow paint. Therefore, we have,
Volume of yellow paint used = 12 litres
So, equating the two expressions for volume of yellow paint used, we get,
$\Rightarrow 3x=12$
Dividing both sides by 3, we get,
$\begin{align}
  & \Rightarrow x=\dfrac{12}{3} \\
 & \therefore x=4 \\
\end{align}$
Now, we have to find the volume of blue paint used by the painter. Since, we have assumed the volume of blue paint used as $2x$, therefore, substituting the value of $x$, we get,
Volume of blue paint used = $2x=2\times 4=8$ litres.

Note:
One may note that we can directly find the volume of blue paint used, by using the expression $\dfrac{3}{2}=\dfrac{12}{a}$, where a is the volume of the blue paint used. Remember that we must write the unit of volume of blue paint used as litres, because the volume of yellow paint used is given in litres only. So, when we will consider the ratio, these units must get cancelled.