55.There were two positive numbers. One of them was increased by $1 \%$, the other by $4 \%$. Could their sum have increased by $3 \%$?
55.Let the first number be $100 x$, and the second $100 y$. We can rephrase the problem as: "Can the equality $101 x + 104 y = 103(x + y)$ hold for some positive $x$ and $y$?", from which it follows that $y = 2x$. For $x = 1$ and $y = 2$, we get the numbers 100 and 200, which will satisfy the condition of the problem.