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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.

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.