What will come in place of question mark (?) in the following questions.
`(((4)/(5)"of 25")/(64))div (432 - 20^(2) + (3)/(7) "of 21") xx (82) = ?"of" (1)/(64)`

Options

A. 50
B. 45
C. 35
D. 40

Answer

To solve the given mathematical expression step by step, we will follow the order of operations (BODMAS/BIDMAS rules: Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

### Given Expression:
\[ \frac{\left(\frac{4}{5} \text{ of } 25\right)}{64} \div \left(432 - 20^2 + \frac{3}{7} \text{ of } 21\right) \times 82 = ? \text{ of } \frac{1}{64} \]

### Step 1: Solve the "of" operations
- **Calculate \( \frac{4}{5} \text{ of } 25 \)**:
\[ \frac{4}{5} \times 25 = \frac{4 \times 25}{5} = \frac{100}{5} = 20 \]

- **Calculate \( \frac{3}{7} \text{ of } 21 \)**:
\[ \frac{3}{7} \times 21 = \frac{3 \times 21}{7} = \frac{63}{7} = 9 \]

### Step 2: Substitute back into the expression
Now the expression can be rewritten as:
\[ \frac{20}{64} \div \left(432 - 400 + 9\right) \times 82 = ? \text{ of } \frac{1}{64} \]

### Step 3: Calculate the expression in the parentheses
- **Calculate \( 432 - 400 + 9 \)**:
\[ 432 - 400 = 32 \quad \text{and then} \quad 32 + 9 = 41 \]

### Step 4: Substitute back into the expression
Now the expression is:
\[ \frac{20}{64} \div 41 \times 82 = ? \text{ of } \frac{1}{64} \]

### Step 5: Solve the division
- **Calculate \( \frac{20}{64} \div 41 \)**:
\[ \frac{20}{64} \div 41 = \frac{20}{64} \times \frac{1}{41} = \frac{20}{64 \times 41} \]

### Step 6: Simplify \( \frac{20}{64} \)
- **Simplify \( \frac{20}{64} \)**:
\[ \frac{20}{64} = \frac{5}{16} \]
So we have:
\[ \frac{5}{16} \div 41 = \frac{5}{16 \times 41} = \frac{5}{656} \]

### Step 7: Multiply by 82
Now we multiply:
\[ \frac{5}{656} \times 82 = \frac{5 \times 82}{656} = \frac{410}{656} \]

### Step 8: Simplify \( \frac{410}{656} \)
- **Find the GCD of 410 and 656**:
The GCD is 82, so:
\[ \frac{410 \div 82}{656 \div 82} = \frac{5}{8} \]

### Step 9: Set equal to \( ? \text{ of } \frac{1}{64} \)
Now we have:
\[ \frac{5}{8} = ? \times \frac{1}{64} \]

### Step 10: Solve for ?
To find \( ? \):
\[ ? = \frac{5}{8} \times 64 = \frac{5 \times 64}{8} = \frac{320}{8} = 40 \]

### Final Answer:
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{40} \]