Question

)") The sum of a two digit number and the number obtained by interchanging its digits
is 99. Find the number.
​

Answer 1

HEY ❤️

Let the digit at unit's place be x and that at ten’s place be y .

 Original number = 10y + x

Reversed number = 10x + y




$10y + x + 10x + y = 99 \\ \\ \\ 11y + 11x = 99 \\ \\ 11(x + y) = 99 \\ \\ x + y = 9..........(1)$


Also, 

When x - y = 3 ---------------- (2)

and x + y = 9

Adding we get 2x = 12


From (1) we get y = 3

Original number = 10y + x

= 36

When x - y = -3 ------------------ (3)

Adding (1) and (3) we get 

and from (1) we get y = 6

Original number = 10y + x

= 63

Hence the number is 36 or 63.