Some equations are solved on the basis of certain system. Find out the correct answer for the unsolved equation on that basis. If `12xx7=408` and `9xx8=207` then `13xx7=?`

Options

A. 190
B. 91
C. 901
D. 109

Explanation

To solve the problem based on the given equations, we need to identify the pattern used in the equations.

1. **Understanding the Pattern:**
- The first equation is \( 12 \times 7 = 408 \).
- The second equation is \( 9 \times 8 = 207 \).
- We need to find \( 13 \times 7 = ? \).

2. **Analyzing the First Equation:**
- Calculate \( 12 \times 7 \):
\[ 12 \times 7 = 84 \]
- The result \( 84 \) is rearranged to form \( 408 \). To do this:
- Reverse the digits of \( 84 \) to get \( 48 \).
- Insert a \( 0 \) between the digits to get \( 408 \).

3. **Analyzing the Second Equation:**
- Calculate \( 9 \times 8 \):
\[ 9 \times 8 = 72 \]
- The result \( 72 \) is rearranged to form \( 207 \). To do this:
- Reverse the digits of \( 72 \) to get \( 27 \).
- Insert a \( 0 \) between the digits to get \( 207 \).

4. **Applying the Same Pattern to the Third Equation:**
- Calculate \( 13 \times 7 \):
\[ 13 \times 7 = 91 \]
- Now, rearranging \( 91 \):
- Reverse the digits of \( 91 \) to get \( 19 \).
- Insert a \( 0 \) between the digits to get \( 109 \).

5. **Final Answer:**
- Therefore, \( 13 \times 7 = 109 \).

### Summary of Steps:
1. Identify the pattern by analyzing the first two equations.
2. Calculate the product of \( 13 \times 7 \).
3. Reverse the digits of the product.
4. Insert a \( 0 \) between the reversed digits.
5. Conclude with the final answer.