Question

A house painter mixes yellow paint with blue paint to get green paint. The ratio of the volumes of the yellow paint to the volume of the blue paint in 5:3, if the difference in volumes of the paints is 500ml, what is the volume of green paint?
(a) 2 litres
(b) 4 litres
(c) 5 litres
(d) 2.5 litres

Answer 1

Hint:
Use a variable to suppose the volumes of yellow paint and blue paint. Now, use the given information to form the equation and to get the value of that variable. Now, get the value of yellow and blue paint and hence volumes of green paint by adding them.


Complete step-by-step answer:
Let us suppose the volumes of yellow paint and blue paint are 5x ml and 3x ml as the given ratio of yellow paint and blue paint as 5:3.
Now, it is given that the difference of volumes of yellow and blue paint is 500ml. so, we can write an equation with the help of this condition as
5x-3x=500
2x=500
Divide the whole equation by ‘2’, we get
$\begin{align}
 & \dfrac{2x}{2}=\dfrac{500}{2} \\
 & \Rightarrow x=250 \\
\end{align}$

So, we can calculate volumes of blue paint and yellow paint by using relations 3x and 5x respectively; where we need to put ‘x = 250’.
Hence, volume of yellow paint is,
$=5x=5\times 250$
$=1250ml$

And, the volume of the blue paint can be given as,
$3x=3\times 250=750ml$

Now, we can determine the volume of green paint by adding the volumes of blue paint and yellow paint as green paint is the mixture of yellow paint and blue paint.
Hence,
Volume of green paint = 750+1250= 2000 ml

Therefore, the volume of the green paint is 2000ml.

Note:
 Writing volumes of yellow paint and blue paint using the given ratio of volumes of both the paints is the key point of the solution. The ratio of 5x and 3x will always be 5:3. Hence, we can use this concept with lots of problems of these kinds.
Volume of the blue paint and yellow paint will remain constant after mixing them. Take care of this statement as well for solving this problem. Only colors will change after mixing, volume will remain constant.