Replace A,B and C by suitable numerals. `({:(," "4CB6),(,+369A):})/(" "8173)`

Answer

To solve the problem of replacing A, B, and C with suitable numerals in the equation \((4CB6) + (369A) = 8173\), we will follow these steps:

### Step 1: Set Up the Equation
We start with the equation:
\[ (4CB6) + (369A) = 8173 \]

### Step 2: Identify the Last Digit
We look at the last digits of both numbers:
- The last digit of \(4CB6\) is \(6\).
- The last digit of \(369A\) is \(A\).

Adding these gives:
\[ 6 + A \equiv 3 \mod 10 \]
This means that \(6 + A\) must end in 3. The possible values for \(A\) can be calculated as follows:
- If \(A = 7\), then \(6 + 7 = 13\) (last digit is 3).

Thus, we have:
\[ A = 7 \]

### Step 3: Substitute A and Analyze the Next Column
Now we substitute \(A\) into the equation:
\[ (4CB6) + (3697) = 8173 \]

### Step 4: Identify the Second Last Digit
Next, we look at the second last digits:
- The second last digit of \(4CB6\) is \(B\).
- The second last digit of \(3697\) is \(9\).

Adding these gives:
\[ B + 9 + 1 \equiv 7 \mod 10 \]
(The \(1\) is the carry from the previous addition of \(6 + 7\)).

This simplifies to:
\[ B + 10 \equiv 7 \mod 10 \]
Thus, \(B\) must be:
\[ B = 7 - 10 = -3 \quad \text{(not possible)} \]
So we try \(B + 9 + 0 \equiv 7 \mod 10\):
\[ B + 9 \equiv 7 \mod 10 \]
This means:
\[ B \equiv 7 - 9 \equiv -2 \equiv 8 \mod 10 \]
Thus, we have:
\[ B = 8 \]

### Step 5: Substitute B and Analyze the Third Column
Now we substitute \(B\) into the equation:
\[ (48C6) + (3697) = 8173 \]

### Step 6: Identify the Third Last Digit
Next, we look at the third last digits:
- The third last digit of \(48C6\) is \(C\).
- The third last digit of \(3697\) is \(6\).

Adding these gives:
\[ C + 6 + 1 \equiv 1 \mod 10 \]
(The \(1\) is the carry from the previous addition of \(B + 9\)).

This simplifies to:
\[ C + 7 \equiv 1 \mod 10 \]
Thus:
\[ C \equiv 1 - 7 \equiv -6 \equiv 4 \mod 10 \]
Thus, we have:
\[ C = 4 \]

### Final Values
Now we have found:
- \(A = 7\)
- \(B = 8\)
- \(C = 4\)

### Conclusion
The values of A, B, and C are:
\[ A = 7, \quad B = 8, \quad C = 4 \]