The sum of the digits of a two - digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
Let the two - digit number be xy (i.e. 10x + y).
After interchanging the digits of the number xy, the new number becomes yx (i.e. 10y + x).
According to question -
x + y = 12.....(1)
(10y + x) - (10x + y) = 18
⇒ - 9x + 9y = 18
⇒ - x + y = 2.....(2)
Adding equations (1) and (2), we get -
y = 7
Substitute the value of y in equation (1), we get -
x = 5
Thus, the required number is 57.