Question

A container filled of milk-water mixture contains 75% milk. 5 litres of this mixture is replaced by water. Next, 10 l of the mixture is replaced by water. If the final percentage of milk in the container is 54%, find the initial quantity of mixture in the container

Answer 1

Let initial quantity of mixture = x liters

Initial quality of milk = 0.75 x liters

So, $0.75x(1-\frac{5}{x})(1-\frac{10}{x})=0.54x$

$\Rightarrow \frac{75}{100}x\left(\frac{x-5}{x}\right)\left(\frac{x-10}{x}\right)=\frac{54x}{100}$

$\Rightarrow 25(x^2-15x+50)=18x^2$

$\Rightarrow 25x^2-375x+1250=0$

$\Rightarrow 7x^2-375x+1250=0$

$x=\frac{375\pm \sqrt{{375}^2-4\times 7\times 1250}}{2\times 7}$

$=\frac{375\pm \sqrt{140625-35000}}{14}$

$=\frac{375+325}{14}=\frac{700}{14},\frac{150}{4}$

$=50,10.7$

$\therefore$ Initial quantity of mixture = 50l.