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The sum of digits of a two-digit number is 15. The number obtained by reversing the order of the digits of the given number exceeds the given number by 9. Find the given number.

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Hint: Make two linear equations in two variables using conditions given in the question.

Let the number be of type $xy$

So, the given number is $10x + y$ actually

Now we have been given that the sum of digits of number is 15
$ \Rightarrow x + y = 15$ -Equation (1)

We are also given that the number obtained by reversing the order of the digits of the given number exceeds the given number by 9

$ \Rightarrow \left( {10y + x} \right) - \left( {10x + y} \right) = 9$
$ \Rightarrow 9y - 9x = 9$
$ \Rightarrow y - x = 1$ -Equation (2)

Adding Equation (1) and Equation (2), we get
$2y = 16$
$ \Rightarrow y = 8$
Putting $y = 8$ in Equation (1) we get
$x + 8 = 15$
$ \Rightarrow x = 7$
As $x = 7$ and $y = 8$
So the given number is 78.

Note: In this question first we assume the digits of the number as x and y. Then using the statements given in the question we formulate two linear equations in two variables and then solve them to get the digits.

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