9.2. In the basket, there are oranges and bananas. If you add as many oranges as there are currently bananas (in pieces), then the percentage of oranges 
will be twice as much as it would be if you added as many bananas as there are currently oranges. What is the current percentage of oranges in the basket?
Answer: 50.

Solution. Let $a$ be the number of oranges, and $b$ be the number of bananas in the basket. If we add as many oranges as there are currently bananas, then there will be $a+b$ oranges out of $a+2b$ fruits, and the proportion of oranges will be $(a+b)/(a+2b)$. If we add as many bananas as there are currently oranges, then there will be $a$ oranges among $2a+b$ fruits, and the proportion of oranges will be $a/(2a+b)$. According to the problem, we have $(a+b)/(a+2b) = 2a/(2a+b)$. From this, we get $b^2 = ab$. Since there are more than zero bananas in the basket, $b = a$, meaning there are an equal number of bananas and oranges in the basket.