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**Hint:**Here, we need to find the difference between the sum and the difference of the digits of the number. Let the digit at ten’s place be \[x\] and the digit at unit’s place be \[y\]. A two-digit number can be written as 10 \[ \times \] the digit at ten’s place \[ + \] the digit at unit’s place. We will write the original and the reversed number in terms of \[x\] and \[y\]. Then, using the given information, we can form two linear equations in two variables. We will solve these equations to find the values of \[x\] and \[y\], and thus, the original two digit number. Finally, we will use the digits to find the difference between the sum and the difference of the digits of the number.

**Complete step-by-step answer:**We will use two variables \[x\] and \[y\] to form a linear equation in two variables using the given information.

A two-digit number can be written as 10 \[ \times \] the digit at ten’s place \[ + \] the digit at unit’s place.

For example, 28 can be written as \[2 \times 10 + 8\].

Let the digit at ten’s place be \[x\] and the digit at the unit's place be \[y\].

Assume that \[x > y\].

Therefore, we get the first number as

\[10 \times x + y = 10x + y\]

When the digits are interchanged, the digit at ten’s place becomes \[y\] and the digit at unit’s place becomes \[x\].

We can write the number when the digits are interchanged as

\[10 \times y + x = 10y + x\]

Now, it is given that the difference between the two digit number and the number obtained by interchanging the digits is 36.

Thus, we get

\[ \Rightarrow \left( {10x + y} \right) - \left( {10y + x} \right) = 36\]

Simplifying the expression, we get

\[ \Rightarrow 10x + y - 10y - x = 36\]

Adding and subtracting the like terms, we get

\[ \Rightarrow 9x - 9y = 36\]

Factoring the number 9, we get

\[ \Rightarrow 9\left( {x - y} \right) = 36\]

Dividing both sides of the equation by 9, we get

\[ \Rightarrow x - y = 4 \ldots \ldots \ldots \left( 1 \right)\]

It is given that the ratio of the digits of the two digit number is 1: 2.

Since \[x > y\], we get

\[ \Rightarrow y:x = 1:2\]

Rewriting the equation, we get

\[ \Rightarrow \dfrac{y}{x} = \dfrac{1}{2}\]

Multiplying both sides of the equation by 2, we get

\[ \Rightarrow 2y = x\]

Rewriting the equation, we get

\[ \Rightarrow x = 2y \ldots \ldots \ldots \left( 2 \right)\]

We can observe that the equations \[\left( 1 \right)\] and \[\left( 2 \right)\] are a pair of linear equations in two variables.

We will solve the equations to find the values of \[x\] and \[y\].

Substituting \[x = 2y\] in equation \[\left( 1 \right)\], we get

\[ \Rightarrow 2y - y = 4\]

Subtracting the like terms, we get

\[\therefore y = 4\]

Substituting \[y = 4\] in the equation \[x = 2y\], we get

\[ \Rightarrow x = 2\left( 4 \right)\]

Multiplying the terms in the expression, we get

\[\therefore x = 8\]

Therefore, we get the original two digit number as

\[10x + y = 10\left( 8 \right) + 4 = 80 + 4 = 84\]

Now, we will find the sum and difference of the digits.

Adding the digits of the number 84, we get

Sum of digits \[ = 8 + 4 = 12\]

Subtracting the digits of the number 84, we get

Difference of digits \[ = 8 - 4 = 4\]

Finally, subtracting the difference of the digits from the sum of the digits, we get

Difference between the sum and the difference of the digits of the number \[ = 12 - 4 = 8\]

Therefore, we get the difference between the sum and the difference of the digits of the number as 8.

**Thus, the correct option is option (b).**

**Note:**We have formed two linear equations in two variables and simplified them to find the number. A linear equation in two variables is an equation of the form \[ax + by + c = 0\], where \[a\] and \[b\]are not equal to 0. For example, \[2x - 7y = 4\] is a linear equation in two variables.

We can verify our answer by using the given information.

The number obtained by reversing the digits of 84 is 48.

We can observe that \[84 - 48 = 36\].

Thus, the difference of the number and the number formed by interchanging the digits is 36.

The ratio of the digits 4 and 8 is 1: 2.

Hence, we have verified our answer.

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