# Mixture and Ratio

A container has two liquids $A$ and $B$ in certain ratio. $10\%$ of the mixture is taken out and replaced with liquid $B$. Now , the ratio of $A$ and $B$ become $2:3$. What was the initial ratio of $A$ and $B$ in the mixture?

Let us assume there is 2 units of A and 3 units of B. If 10% of A was there previously, then there was $\frac1{1-0.1}\cdot2$ units of A (We take the inverse of the percentage of how much there is now compared to originally). This comes to $2\frac29$. So $2\frac29-2=\frac29$ of liquid B was added to replace the $\frac29$ units of A missing. That means there were originally $3-\frac29=2\frac79$ units of liquid B. Therefore, the ratio between A and B is $2\frac29:2\frac79=20:25=4:5$