When a 2 digit number(x) is reversed, the number so formed is 63 more than the original number. If the sum of digits of original number is 11, then find the value of x + 15 ?

Options

A. A)48
B. B)44
C. C)36
D. D)56

Answer

To solve the problem step by step, we will denote the two-digit number as \( x \), where \( x \) can be expressed in terms of its digits. Let's denote the tens digit as \( a \) and the units digit as \( b \). Therefore, we can express \( x \) as:

\[ x = 10a + b \]

### Step 1: Set up the equation for the reversed number
When the digits of the number are reversed, the new number becomes:

\[ 10b + a \]

According to the problem, this reversed number is 63 more than the original number. Therefore, we can set up the following equation:

\[ 10b + a = (10a + b) + 63 \]

### Step 2: Simplify the equation
Now, let's simplify the equation:

\[ 10b + a = 10a + b + 63 \]

Subtract \( b \) and \( a \) from both sides:

\[ 10b - b + a - a = 10a - a + 63 \]

This simplifies to:

\[ 9b - 9a = 63 \]

Dividing the entire equation by 9 gives us:

\[ b - a = 7 \quad \text{(Equation 1)} \]

### Step 3: Set up the equation for the sum of digits
We are also given that the sum of the digits \( a \) and \( b \) is 11:

\[ a + b = 11 \quad \text{(Equation 2)} \]

### Step 4: Solve the system of equations
Now we have a system of two equations:

1. \( b - a = 7 \)
2. \( a + b = 11 \)

From Equation 1, we can express \( b \) in terms of \( a \):

\[ b = a + 7 \]

Now, substitute this expression for \( b \) into Equation 2:

\[ a + (a + 7) = 11 \]

This simplifies to:

\[ 2a + 7 = 11 \]

Subtract 7 from both sides:

\[ 2a = 4 \]

Dividing by 2 gives:

\[ a = 2 \]

### Step 5: Find the value of \( b \)
Now, substitute \( a = 2 \) back into the expression for \( b \):

\[ b = 2 + 7 = 9 \]

### Step 6: Find the original number \( x \)
Now that we have both digits, we can find the original number \( x \):

\[ x = 10a + b = 10(2) + 9 = 20 + 9 = 29 \]

### Step 7: Find \( x + 15 \)
Finally, we need to find the value of \( x + 15 \):

\[ x + 15 = 29 + 15 = 44 \]

Thus, the final answer is:

\[ \boxed{44} \]