The correct option is 1375.

To find the value that replaces the question mark (?), we need to perform the interchanged operations as specified in the problem statement:
1. '+' and '–' are interchanged (i.e., replace '+' with '–' and replace '–' with '+').
2. '×' and '÷' are interchanged (i.e., replace '×' with '÷' and replace '÷' with '×').

The given equation is:
$4515\times 5-431÷3+821=?$

After interchanging the operators, the equation becomes:
$4515÷5+431\times 3-821=?$

Now, we solve the expression using the standard BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction) rule:

Step 1: Perform Division
Divide 4515 by 5:
$4515÷5=903$

Substitute this back into the equation:
$903+431\times 3-821=?$

Step 2: Perform Multiplication
Multiply 431 by 3:
$431\times 3=1293$

Substitute this value:
$903+1293-821=?$

Step 3: Perform Addition
Add 903 and 1293:
$903+1293=2196$

Substitute this value:
$2196-821=?$

Step 4: Perform Subtraction
Subtract 821 from 2196:
$2196-821=1375$

Therefore, the value that replaces the question mark is 1375.