Question

The sum of the digits of a 2 digit number is 17 on reversing the digits the number formed is 9 more than the original number find the original number.

Answer 1

let the first digit be x
and second digit be y

so the number is 10x+y

according to the condition of the question

x+y=17. (1)

according to the second condition of the question

10y+x=9+10x+y

10y-y+x-10x=9

9y-9x=9

on dividing whole equation by 9

y-x=1

x-y=-1. (2)

eq. (1)+(2)

y will be cancelled and x+x=2x


2x=16

x=16/2

x=8

putting in eq. (2)

8-y=-1

y=8+1

y=9


so the original number is 10x+y

=10*8+9

=80+9

=89