1. Before the sale, a spoon and a fork cost the same. During the sale, the price of the spoon was reduced by 1 ruble, and the price of the fork was reduced to one-tenth of its original price. Could it happen that the spoon was sold cheaper than the fork during the sale?
Answer: It could. Solution. Let the initial price be 1 p. 10 kop. Then on sale, the spoon cost 10 kop., and the fork - 11 kop. Remark. Let $x$ be the initial price in kopecks. Then $x$ must be greater than 100 (since the sale price of the spoon must be positive), divisible by 10 (since the sale price of the fork must be expressed as a positive integer number of kopecks), and satisfy the inequality $x-100100$ and no other meaningful progress - 2 points.