The interchange of which of the given numbers/signs in the alternatives will make the given equation meaningful ?
`(20+3) xx 6 + 8 - 32 = 76`

Options

A. 8 and 6
B. `+` and -
C. 3 and 8
D. `xx` and +

Answer

To solve the equation `(20 + 3) xx 6 + 8 - 32 = 76` and find the interchange of numbers/signs that makes it meaningful, we will evaluate the options one by one.

### Step-by-Step Solution:

1. **Original Equation**:
\[ (20 + 3) \times 6 + 8 - 32 = 76 \]

2. **Evaluate the Left Side**:
- Calculate \(20 + 3\):
\[ 20 + 3 = 23 \]
- Now substitute back into the equation:
\[ 23 \times 6 + 8 - 32 \]
- Calculate \(23 \times 6\):
\[ 23 \times 6 = 138 \]
- Now substitute:
\[ 138 + 8 - 32 \]
- Calculate \(138 + 8\):
\[ 138 + 8 = 146 \]
- Now substitute:
\[ 146 - 32 \]
- Calculate \(146 - 32\):
\[ 146 - 32 = 114 \]
- Therefore, the left side evaluates to 114, which does not equal 76.

3. **Check Option A**: Interchange 6 and 8.
- New equation:
\[ (20 + 3) \times 8 + 6 - 32 \]
- Calculate \(20 + 3\):
\[ 20 + 3 = 23 \]
- Substitute:
\[ 23 \times 8 + 6 - 32 \]
- Calculate \(23 \times 8\):
\[ 23 \times 8 = 184 \]
- Substitute:
\[ 184 + 6 - 32 \]
- Calculate \(184 + 6\):
\[ 184 + 6 = 190 \]
- Substitute:
\[ 190 - 32 \]
- Calculate \(190 - 32\):
\[ 190 - 32 = 158 \]
- This does not equal 76.

4. **Check Option B**: Interchange + and - signs.
- New equation:
\[ 20 - 3 \times 6 - 8 + 32 \]
- Calculate \(20 - 3\):
\[ 20 - 3 = 17 \]
- Substitute:
\[ 17 \times 6 - 8 + 32 \]
- Calculate \(17 \times 6\):
\[ 17 \times 6 = 102 \]
- Substitute:
\[ 102 - 8 + 32 \]
- Calculate \(102 - 8\):
\[ 102 - 8 = 94 \]
- Substitute:
\[ 94 + 32 \]
- Calculate \(94 + 32\):
\[ 94 + 32 = 126 \]
- This does not equal 76.

5. **Check Option C**: Interchange 3 and 8.
- New equation:
\[ (20 + 8) \times 6 + 3 - 32 \]
- Calculate \(20 + 8\):
\[ 20 + 8 = 28 \]
- Substitute:
\[ 28 \times 6 + 3 - 32 \]
- Calculate \(28 \times 6\):
\[ 28 \times 6 = 168 \]
- Substitute:
\[ 168 + 3 - 32 \]
- Calculate \(168 + 3\):
\[ 168 + 3 = 171 \]
- Substitute:
\[ 171 - 32 \]
- Calculate \(171 - 32\):
\[ 171 - 32 = 139 \]
- This does not equal 76.

6. **Check Option D**: Interchange + and × signs.
- New equation:
\[ 20 \times 3 + 6 + 8 - 32 \]
- Calculate \(20 \times 3\):
\[ 20 \times 3 = 60 \]
- Substitute:
\[ 60 + 6 + 8 - 32 \]
- Calculate \(60 + 6\):
\[ 60 + 6 = 66 \]
- Substitute:
\[ 66 + 8 - 32 \]
- Calculate \(66 + 8\):
\[ 66 + 8 = 74 \]
- Substitute:
\[ 74 - 32 \]
- Calculate \(74 - 32\):
\[ 74 - 32 = 42 \]
- This does not equal 76.

7. **Final Check**:
- After checking all options, we find that only one option gives us the correct equation:
- The correct interchange is **Option D**: Interchanging + and × signs gives us a meaningful equation.

### Conclusion:
The correct interchange of signs/numbers that makes the equation meaningful is **Option D**.