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.
`5 + 6 -: 3 - 12 xx 2 = 17`

Options

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

Explanation

To solve the equation \( 5 + 6 -: 3 - 12 \times 2 = 17 \) and find the correct alternative by interchanging two signs, we will follow these steps:

### Step 1: Understand the Original Equation
The original equation is:
\[ 5 + 6 -: 3 - 12 \times 2 = 17 \]
Here, the operation "-:" indicates division. Thus, we can rewrite the equation as:
\[ 5 + 6 \div 3 - 12 \times 2 = 17 \]

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

### Step 3: Check the Current Equation
Let's evaluate the left-hand side of the equation:
1. First, perform the division:
\[ 6 \div 3 = 2 \]
2. Now substitute back into the equation:
\[ 5 + 2 - 12 \times 2 \]
3. Next, perform the multiplication:
\[ 12 \times 2 = 24 \]
4. Substitute again:
\[ 5 + 2 - 24 \]
5. Now, perform the addition:
\[ 5 + 2 = 7 \]
6. Finally, perform the subtraction:
\[ 7 - 24 = -17 \]

The left-hand side evaluates to \(-17\), which does not equal \(17\). Thus, the equation is incorrect.

### Step 4: Identify the Interchange of Signs
We need to find which two signs can be interchanged to make the equation correct. The options typically involve switching the division with multiplication or addition with subtraction.

### Step 5: Test the First Option (Interchange Division and Multiplication)
Let's interchange the division sign with the multiplication sign:
\[ 5 + 6 \times 3 - 12 \div 2 \]

1. Perform the multiplication:
\[ 6 \times 3 = 18 \]
2. Substitute back:
\[ 5 + 18 - 12 \div 2 \]
3. Now perform the division:
\[ 12 \div 2 = 6 \]
4. Substitute again:
\[ 5 + 18 - 6 \]
5. Perform the addition:
\[ 5 + 18 = 23 \]
6. Finally, perform the subtraction:
\[ 23 - 6 = 17 \]

Now, the left-hand side equals \(17\), which matches the right-hand side.

### Conclusion
The correct alternative is to interchange the division sign with the multiplication sign. Thus, the correct answer is the first option.

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