Q. 133.8( 16 Votes )

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.

Answer :

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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