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.
`16 - 8 -: 4+5 xx 2 = 8`

Options

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

Explanation

To solve the equation \( 16 - 8 -: 4 + 5 \times 2 = 8 \) and find the correct alternative by interchanging two signs, we will follow these steps:

### Step 1: Understand the Original Equation
The original equation is:
\[ 16 - 8 -: 4 + 5 \times 2 = 8 \]

### Step 2: Identify the Operations
In the equation, we have:
- Subtraction (-)
- Division (-:)
- Addition (+)
- Multiplication (×)

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

### Step 4: Check the Current Equation
Let's evaluate the left side of the equation:
\[ 16 - 8 -: 4 + 5 \times 2 \]

1. **Division**: First, we need to perform the division:
\[ 8 -: 4 = 2 \]
So, the equation becomes:
\[ 16 - 2 + 5 \times 2 \]

2. **Multiplication**: Next, perform the multiplication:
\[ 5 \times 2 = 10 \]
Now, the equation looks like:
\[ 16 - 2 + 10 \]

3. **Subtraction and Addition**: Now, we perform subtraction and addition from left to right:
\[ 16 - 2 = 14 \]
\[ 14 + 10 = 24 \]

Thus, the left side evaluates to 24, which is not equal to 8.

### Step 5: Identify the Correct Interchange of Signs
We need to find which interchange of signs will make the equation correct.

#### Option 1: Interchange Division with Multiplication
If we interchange division (-:) with multiplication (×):
\[ 16 - 8 \times 4 + 5 -: 2 \]

1. **Multiplication**:
\[ 8 \times 4 = 32 \]
The equation becomes:
\[ 16 - 32 + 5 -: 2 \]

2. **Division**:
\[ 5 -: 2 = 2.5 \]
Now, the equation looks like:
\[ 16 - 32 + 2.5 = -15.5 \] (not equal to 8)

#### Option 2: Interchange Minus with Division
If we interchange minus (-) with division (-:):
\[ 16 -: 8 - 4 + 5 \times 2 \]

1. **Division**:
\[ 16 -: 8 = 2 \]
The equation becomes:
\[ 2 - 4 + 5 \times 2 \]

2. **Multiplication**:
\[ 5 \times 2 = 10 \]
Now, the equation looks like:
\[ 2 - 4 + 10 \]

3. **Subtraction and Addition**:
\[ 2 - 4 = -2 \]
\[ -2 + 10 = 8 \] (this is equal to 8)

### Conclusion
The correct option is to interchange minus with division, which makes the equation valid.

### Final Answer
The correct alternative is **Option 2**.