Certain equations are based on a certain system. Find out the correct answer for unsolved equation on that basis:
If `14xx13=128` and `16xx13=280` then `15xx11=?`

Options

A. (a) 516
B. (b) 156
C. (c) 165
D. (d) 615

Explanation

To solve the equation based on the given pattern, we can follow these steps:

### Step 1: Identify the pattern
We need to analyze the given equations to find a consistent pattern. The equations provided are:
1. \( 14 \times 13 = 128 \)
2. \( 16 \times 13 = 280 \)

### Step 2: Calculate the products
Let's calculate the products of the first numbers with 13:
- For the first equation:
\[ 14 \times 13 = 182 \]
- For the second equation:
\[ 16 \times 13 = 208 \]

### Step 3: Compare the results with the given outputs
Now, let's compare these calculated products with the outputs given in the equations:
- The output for \( 14 \times 13 \) is \( 128 \). If we look closely, \( 182 \) can be rearranged to \( 128 \) by swapping the digits \( 8 \) and \( 2 \).
- The output for \( 16 \times 13 \) is \( 280 \). Similarly, \( 208 \) can be rearranged to \( 280 \) by swapping the digits \( 0 \) and \( 8 \).

### Step 4: Apply the same pattern to the new equation
Now, we need to apply the same pattern to the equation \( 15 \times 11 \):
- First, calculate \( 15 \times 11 \):
\[ 15 \times 11 = 165 \]

### Step 5: Rearrange the digits
Following the established pattern, we will swap the digits \( 6 \) and \( 5 \) in \( 165 \) to get \( 156 \).

### Final Answer
Thus, the answer to \( 15 \times 11 \) based on the established pattern is:
\[ \boxed{156} \]