sum of the digits of a two digit number is 9 . the number obtained by interchanging the digits exceeds the given number by 27 . find the original number
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Let the two digit number be 10x+y.
Given that the sum of the digits is 9 x+y=9 .
Given that the number obtained by interchanging the digits exceeds the given number by 27
10y+x=10x+y+27
9x−9y=−27
On taking 9 as common
x−y=−3 .
Adding equation (1) and (2)
x+y=9
x−y=−3
2x=6
x=3
3+y=9
y=6
Therefore, the number is 10x+y is 36.
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