In each of the following questions, an equation becomes incorrect due to the interchange of two signs. One of the four alternatives under it specifies the interchange of signs in the equation, which when made will make the equation correct. Find the correct alternative.
`9 + 5-: 4 xx 3 - 6 = 12`

Options

A. `+` and `xx`
B. `-:` and ` xx`
C. `-:` and -
D. `+` and -

Explanation

To solve the equation \( 9 + 5 -: 4 \times 3 - 6 = 12 \) and determine which sign interchange makes it correct, we will analyze the equation step by step.

### Step 1: Understand the Original Equation
The original equation is:
\[ 9 + 5 -: 4 \times 3 - 6 = 12 \]
Here, the operation "-:" represents division. Thus, we can rewrite the equation as:
\[ 9 + 5 \div 4 \times 3 - 6 = 12 \]

### Step 2: Apply BODMAS/BIDMAS Rule
According to the BODMAS/BIDMAS rule, we need to perform operations in the following order:
1. Brackets
2. Orders (i.e., powers and roots, etc.)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

### Step 3: Calculate the Left Side of the Equation
Let's calculate the left side of the equation step by step:
1. **Division**: \( 5 \div 4 = 1.25 \)
2. **Multiplication**: \( 1.25 \times 3 = 3.75 \)
3. **Addition**: \( 9 + 3.75 = 12.75 \)
4. **Subtraction**: \( 12.75 - 6 = 6.75 \)

So, the left side evaluates to \( 6.75 \), which does not equal \( 12 \).

### Step 4: Identify Possible Interchanges
We need to check each option provided to see which interchange of signs will make the equation correct.

1. **Option 1**: Interchange "+" with "×"
- New equation: \( 9 \times 5 -: 4 + 3 - 6 \)
- Calculate: \( 9 \times 5 = 45 \), then \( 45 \div 4 + 3 - 6 \) does not equal \( 12 \).

2. **Option 2**: Interchange "−:" with "×"
- New equation: \( 9 + 5 \times 4 - 3 - 6 \)
- Calculate: \( 9 + 20 - 3 - 6 = 20 \), does not equal \( 12 \).

3. **Option 3**: Interchange "−:" with "−"
- New equation: \( 9 + 5 - 4 \times 3 -: 6 \)
- Calculate: \( 9 + 5 - 12 \div 6 = 9 + 5 - 2 = 12 \), which equals \( 12 \).

4. **Option 4**: Interchange "×" with "−"
- New equation: \( 9 + 5 -: 4 - 3 - 6 \)
- Calculate: \( 9 + 5 - 4 - 3 - 6 \) does not equal \( 12 \).

### Conclusion
The correct alternative is **Option 3**, where we interchange the division sign with the subtraction sign.