Question

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of a mixture such that the ratio of water to milk in that mixture is 3: 5?

Answer 1

Let x and (12-x) litres of milk be mixed from the first and second container respectivelyAmount of milk in x litres of the the first container= .75xAmount of water in x litres of the the first container = .25xAmount of milk in (12-x) litres of the the second container = .5(12-x)Amount of water in (12-x) litres of the the second container = .5(12-x)Ratio of water to milk = [.25x + .5(12-x)] : [.75x +.5(12-x)] = 3 : 5$MF#%\begin{align} &\Rightarrow\dfrac{\left(.25x+6-.5x\right)}{\left(.75x+6-.5x\right)}=\dfrac{3}{5}\\\\\\\\ &\Rightarrow\dfrac{\left(6-.25x\right)}{\left(.25x+6\right)}=\dfrac{3}{5}\\\\\\\\ &\Rightarrow 30-1.25x=.75x+18\\\\ &\Rightarrow 2x=12\\\\ &\Rightarrow x=6\end{align}$MF#%Since x = 6, 12-x = 12-6 = 6Hence 6 and 6 litres of milk should mixed from the first and second container respectively