The sum of the digits of a two digit number is 10. The number obtained

1.	The sum of the digits of a two digit number is 10. The number obtained by interchanging the digits exceeds the original number by 36. Find the original number.
Answer» GIVEN:- Sum of the digits of two digit NUMBER is 10. The new number obtained by interchanging the digits EXCEEDS the ORIGINAL number by 36. To Find:- The original number. Solution:- Here, LET the unit digit of the two digit number be $x$ . Sum of the digits = 10 $Tenth \ digit = 10 - Ones \ digit$ Hence, We can write tenth digit number as $10 ( 10 - x )$ . Original number is $x + 10 ( 10 - x )$ After interchanging the digits we get $(10 - x) + 10x$ According to the question, ⇒ $(10 - x) + 10x$ - $[ x + 10 ( 10 - x ) ]$ = 36 ⇒ $10 - x + 10x - x - 100 + 10x = 36$ ⇒ $18x - 90 = 36$ ⇒ $18x = 36 + 90$ ⇒ $x = \dfrac{126}{18}$ ⇒ $x = 7$ Therefore, The original number = $x + 10 ( 10 - x )$ = $7 + 10 ( 10 - 7 )$ [ Putting the value of x ] = 37 Hence, The original number is 37. Verification:- Since, $(10 - x) + 10x$ - $[ x + 10 ( 10 - x ) ]$ = 36 ⇒ $(10 - 7 ) + 10 \times 7 - [ 7 + 10 ( 10 - 7 )] = 36$ [ Putting the value of x ] ⇒ $73 - 37 = 36$ ⇒ $36 = 36$ Hence, From verification the original number is 37 .