The sum of the digits of a two digir number is 7 . The number obtained

1.	The sum of the digits of a two digir number is 7 . The number obtained by interchanging the digits exceeds the original number by 27 . Find the number
Answer» GIVEN: The sum of the digits of a two DIGIT number is 7 The number obtained by INTERCHANGING the digits exceeds the ORIGINAL number by 27 TO FIND: What are the numbers ? SOLUTION: Let the digit at the unit's place be 'y' and the digit at ten's place be 'x' ❒ NUMBER = 10x + y CASE:- 1 The sum of the digits of a two digit number is 7 According to question:- $\bf{\hookrightarrow x + y = 7...1)}$ $\rm{\hookrightarrow x = 7-y }$ CASE:- 2 The number obtained by interchanging the digits exceeds the original number by 27. Number obtained by reversing the digits = 10y + x Number obtained by reversing the digits = Original number + 27 According to question:- $\rm{\hookrightarrow 10y + x = <klux>10X</klux> + y + 27 }$ $\rm{\hookrightarrow -27 = 10x+y-10y-x }$ $\rm{\hookrightarrow -27 = 9x-9y }$ Taking 9 as common from both sides $\bf{\hookrightarrow -3 = x-y....2) }$ Put the value of 'x' in EQUATION 2) $\rm{\hookrightarrow -3 = 7-y-y }$ $\rm{\hookrightarrow -3-7 = -2y }$ $\rm{\hookrightarrow -10 = -2y }$ $\rm{\hookrightarrow \cancel\dfrac{-10}{-2} = y }$ $\bf{\hookrightarrow 5 = y }$ Put the value of 'y' in equation 1) $\rm{\hookrightarrow x + 5 = 7 }$ $\rm{\hookrightarrow x = 7-5 }$ $\bf{\hookrightarrow x = 2 }$ Number = 10x + y Number = 10(2)+5 Number = 20+5 Number = 25 ❝ Hence, the number is 25 ❞ ______________________