Problem #PRU-100537

Problems Number Theory Arithmetic operations. Number identities

Problem

Jane wrote another number on the board. This time it was a two-digit number and again it did not include digit \(5\). Jane then decided to include it, but the number was written too close to the edge, so she decided to fit the \(5\) in between the two digits. She noticed that the resulting number is \(11\) times larger than the original. What is the sum of digits of the new number?