The value of `25 - 5 [2 + 3 (2 - 2(5 - 3) + 5) - 10] div 4` is :

Options

A. 5
B. 23.25
C. 23.75
D. 25

Answer

To solve the expression \( 25 - 5 [2 + 3 (2 - 2(5 - 3) + 5) - 10] \div 4 \), we will follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

### Step-by-Step Solution:

1. **Evaluate the innermost parentheses**:
\[ 5 - 3 = 2 \]
Now, substitute this back into the expression:
\[ 25 - 5 [2 + 3 (2 - 2 \cdot 2 + 5) - 10] \div 4 \]

2. **Substitute and simplify inside the brackets**:
\[ 2 - 2 \cdot 2 + 5 \]
First, calculate \( 2 \cdot 2 = 4 \):
\[ 2 - 4 + 5 = 3 \]
Now, substitute this back into the expression:
\[ 25 - 5 [2 + 3 \cdot 3 - 10] \div 4 \]

3. **Multiply**:
\[ 3 \cdot 3 = 9 \]
Substitute back:
\[ 25 - 5 [2 + 9 - 10] \div 4 \]

4. **Simplify inside the brackets**:
\[ 2 + 9 - 10 = 1 \]
Substitute back:
\[ 25 - 5 [1] \div 4 \]

5. **Evaluate the brackets**:
\[ 5 [1] = 5 \]
Now, substitute back:
\[ 25 - 5 \div 4 \]

6. **Perform the division**:
\[ 5 \div 4 = 1.25 \]
Substitute back:
\[ 25 - 1.25 \]

7. **Final subtraction**:
\[ 25 - 1.25 = 23.75 \]

### Final Answer:
The value of the expression is \( 23.75 \).

---