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Question

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

Solution
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Let the two digit number be 10x+y
Given that the sum of the digits is 9
x+y=9------------------(1))
Given that the number obtained by interchanging the digits exceeds the given number by 27
10y+x=10x+y+27
9x9y=27
taking 9 as common
xy=3---------------------(2)
Adding equation 1 and 2
x+y=9
xy=3
2x=6
x=3
3+y=9
y=6
The number is 10x+y is 36.

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