Some equations are solved on the basis of certain system. Find out the corrct answer for the unsolved equation on that basis.
If `12xx9=810` and `15xx9=513` then `13xx8`=?`

Options

A. 104
B. 410
C. 401
D. 411

Explanation

To solve the problem, we need to identify the pattern used in the given equations. Let's break it down step by step.

### Given Equations:
1. \( 12 \times 9 = 810 \)
2. \( 15 \times 9 = 513 \)

### Step 1: Analyze the First Equation
For the equation \( 12 \times 9 = 810 \):
- The actual multiplication \( 12 \times 9 = 108 \).
- The result given is \( 810 \).
- If we look closely, the digits of \( 108 \) have been rearranged to form \( 810 \). Specifically, the last digit (8) is moved to the front, followed by the first digit (1), and then the second digit (0).

### Step 2: Analyze the Second Equation
For the equation \( 15 \times 9 = 513 \):
- The actual multiplication \( 15 \times 9 = 135 \).
- The result given is \( 513 \).
- Again, if we rearrange the digits of \( 135 \), we can see that the last digit (5) is moved to the front, followed by the first digit (1), and then the second digit (3).

### Step 3: Identify the Pattern
From the above two equations, we can deduce the pattern:
- The result of the multiplication is rearranged such that the last digit comes first, followed by the first digit, and then the second digit.

### Step 4: Apply the Pattern to the New Equation
Now, we need to find \( 13 \times 8 \):
- First, calculate \( 13 \times 8 = 104 \).

### Step 5: Rearranging the Digits
Now, rearranging the digits of \( 104 \):
- The last digit (4) comes first, followed by the first digit (1), and then the second digit (0).
- So, the rearranged result would be \( 410 \).

### Final Answer
Thus, \( 13 \times 8 = 410 \).

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