# The sum of the digits of a two - digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. 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 = 15.....(1)

(10y + x) - (10x + y) = 9

- 9x + 9y = 9

- x + y = 1.....(2)

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

y = 8

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

x = 7

Thus, the required number is 78.

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