Question

the sum of the digit of a two digit number is 8 the number obtained by interchanging the digit exceeds the given number by 18 give find the given number

Answer 1

Let the two digits number be 10x + y

Given that the sum of their digits is 8

=> x + y = 8

Also given that when we reverse it, the new number exceeds the older by 18

Reverse of the number = 10y + x

=> 10y + x = 10x + y + 18

°> 10y + x - 10x - y = 18

=> 9y - 9x = 18

=> 9(y - x) = 18

=> y - x = 18/9

=> y - x = 2

and y + x = 8

Add the two equations

=> y - x + y + x = 2 + 8

=> 2y = 10

=> y = 10/2

=> y = 5

So y - x = 2

=> 5 - x = 2

=> - x = 2 - 5

=> - x = - 3

=> x = 3

Hence, the two digits number = 10x + y

= 10(3) + 5

= 30 + 5

= 35


Answer :- 35