1. A third of the stock was sold at a price that is $10\%$ higher than the planned price, and half of the stock was sold for $15\%$ cheaper than the planned price. By what percentage above the planned price was the remaining stock sold, if in the end, the revenue collected is what would have been obtained if the entire quantity of stock had been sold at the planned price?
Solution. Let $x$ be the percentage at which the remaining stock needs to be sold above the planned price. Then $\frac{1}{3} \cdot 1.1 + \frac{1}{2} \cdot 0.85 + \frac{1}{6} x = 1$, from which we get $x = 1.25$, which means the remaining stock was sold at a 25% higher price.