A two digit number is such that sum of the ones and tens digit is 10.If the digits are reversed, the new number formed exceeds the original number by 54. Find the new number
Let the tens digit of the original number be x and the ones digit be y. The original number is 10x + y, and the new number formed by reversing the digits is 10y + x.Since the new number exceeds the original number by 54, we can set up the equation:10y + x = 10x + y + 549x – 9y = 54x – y = 6Since x and y are both digits, they must both be integers. The only solution to this equation that satisfies this condition is x = 8 and y = 2.Therefore, the original number is 82 and the new number formed by reversing the digits is 28. This is the new number.