Question

sum of two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 54 find the original number

Answer 1

Given sum of the digits is 12
Let the digits in ones place be x
Hence the digit in tens place is (12 – x)
The original number = 10(12 – x) + x = 120 – 9x
Number formed by reversing the digits = 10x + (12 – x)  =  9x + 12
Given that number formed by reversing the digits is 54 greater than the original number.
⇒ 9x + 12 = (120 – 9x) + 54 = 174 – 9x
⇒ 18x = 174 – 12 = 162
∴ x = 9
The original number = 120 – 9x = 120 – 9(9) = 39