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Question

The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

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Solution

Let the number at the ten's place be x and that at the one's place be y.
Number obtained = 10x + y
The sum of the digits in a two-digits number is 9.
x+y=9 .....(I)
The number obtained by interchanging the digits exceeds the original number by 27.
10y+x-10x + y=2710y+x-10x-y=279y-9x=27y-x=3 .....II
Adding (I) and (II)
2y=12y=6
x = 3
Thus, the number is 36.

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