Replace A,B and C by suitable numerals. `({:(," "A),(,+A),(," "A):})/(" "BA)`

Answer

To solve the problem `({:(," "A),(,+A),(," "A):})/(" "BA)`, we need to replace A, B, and C with suitable numerals.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression can be interpreted as:
\[ \frac{A + A + A}{BA} \]
Here, \(BA\) represents a two-digit number where B is the tens place and A is the units place.

2. **Simplifying the Numerator**:
Since \(A + A + A\) is the same as \(3A\), we can rewrite the expression as:
\[ \frac{3A}{BA} \]

3. **Expressing BA**:
The two-digit number \(BA\) can be expressed as:
\[ BA = 10B + A \]

4. **Setting Up the Equation**:
Now we can set up the equation:
\[ \frac{3A}{10B + A} = 1 \]
This means that \(3A\) must equal \(10B + A\).

5. **Rearranging the Equation**:
Rearranging gives us:
\[ 3A - A = 10B \]
Simplifying this leads to:
\[ 2A = 10B \]
or
\[ A = 5B \]

6. **Finding Suitable Values**:
Since A and B must be single-digit numbers (0-9), we can find suitable values for A and B:
- If \(B = 1\), then \(A = 5 \times 1 = 5\).
- If \(B = 2\), then \(A = 5 \times 2 = 10\) (not valid since A must be a single digit).

Therefore, the only valid solution is:
- \(B = 1\)
- \(A = 5\)

7. **Determining C**:
Since C does not appear in the equation, we can assign:
\[ C = 0 \]

### Final Values:
- A = 5
- B = 1
- C = 0