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 -

sum of the digits is 12

⇒ x + y = 12.....(1)

Also, the number obtained by interchanging its digits exceeds the given number by 18

⇒ (10y + x) - (10x + y) = 18

- 9x + 9y = 18

- x + y = 2.....(2)

Adding equations (1) and (2), we get -

x + y - x + y = 10 + 4
⇒ 2y = 14
⇒ y = 7

Substitute the value of y in equation (1), we get -

x = 5

Thus, the required number is 57.

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