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.
`72 + 12 xx 3 -:8 - 6 = 20`

Options

A. + and x
B. + and ÷
C. ÷ and -
D. + and -

Explanation

To solve the equation \(72 + 12 \times 3 -: 8 - 6 = 20\) by interchanging two signs, we will evaluate each option provided to find the correct one.

### Step-by-Step Solution:

1. **Identify the Original Equation**:
The original equation is:
\[ 72 + 12 \times 3 -: 8 - 6 = 20 \]

2. **Evaluate Each Option**:

**Option 1**: Interchange the signs of plus and multiply.
\[ 72 \times 12 + 3 -: 8 - 6 \]
- Solve:
- First, perform the division:
\[ 72 \times 12 + 3 \div 8 - 6 \]
- Calculate \(72 \times 12 = 864\):
\[ 864 + 3 \div 8 - 6 \]
- Next, calculate \(3 \div 8 = 0.375\):
\[ 864 + 0.375 - 6 = 858.375 \quad (\text{not } 20) \]

**Option 2**: Interchange the signs of plus and divide.
\[ 72 -: 12 \times 3 + 8 - 6 \]
- Solve:
- First, perform the division:
\[ 72 \div 12 \times 3 + 8 - 6 \]
- Calculate \(72 \div 12 = 6\):
\[ 6 \times 3 + 8 - 6 \]
- Next, calculate \(6 \times 3 = 18\):
\[ 18 + 8 - 6 \]
- Finally, calculate \(18 + 8 = 26\) and \(26 - 6 = 20 \quad (\text{correct})\)

**Option 3**: Interchange the signs of divide and minus.
\[ 72 + 12 \times 3 \div 6 - 8 \]
- Solve:
- First, perform the division:
\[ 72 + 12 \times 3 \div 6 - 8 \]
- Calculate \(12 \times 3 = 36\):
\[ 72 + 36 \div 6 - 8 \]
- Next, calculate \(36 \div 6 = 6\):
\[ 72 + 6 - 8 \]
- Finally, calculate \(72 + 6 = 78\) and \(78 - 8 = 70 \quad (\text{not } 20) \] **Option 4**: Interchange the signs of plus and minus. \[ 72 - 12 \times 3 -: 8 + 6 \] - Solve: - First, perform the division: \[ 72 - 12 \times 3 \div 8 + 6 \] - Calculate \(12 \times 3 = 36\):
\[ 72 - 36 \div 8 + 6 \]
- Next, calculate \(36 \div 8 = 4.5\):
\[ 72 - 4.5 + 6 \]
- Finally, calculate \(72 - 4.5 = 67.5\) and \(67.5 + 6 = 73.5 \quad (\text{not } 20)
\]

3. **Conclusion**:
The only option that makes the equation correct is **Option 2**.