Question

sum of a two digit number is 9. when we interchange the digits it is found that the resulting new number is greater than orignal number by 27 what is the two digit number

Answer 1

Assume the digit in ones place as x and the digit in tens place is yThe original number is (10y + x)Number obtained by reversing the digits = (10x + y)Now check for the conditionGiven that sum of digits of the number is 9That is x + y = 9   → (1)Second condition is, number obtained by interchanging the digits is greater than the original number by 27That is (10x + y) = (10y + x) 27⇒ 10x + y – 10y – x = 27⇒ 9x – 9y  = 27∴ x – y = 3 → (2)Add (1) and (2), we getx + y = 9x – y = 3-----------2x = 12∴ x = 6Put x = 6 in (1), we get6 + y = 9⇒ y = 9 – 6 = 3The original number = 10y + x = 10(3) + 6 = 36