The value of `(120 div (5)/(4)) - {(105 - 5 xx 3 + 2 " of " 17 div (1)/(6)) div (5 + (1)/(4))}` is

Options

A. 46
B. 50
C. 45
D. 40

Answer

To solve the expression `(120 div (5)/(4)) - {(105 - 5 xx 3 + 2 " of " 17 div (1)/(6)) div (5 + (1)/(4))}`, we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the expression**:
\[ (120 \div (5)/(4)) - \left\{(105 - 5 \times 3 + 2 \text{ of } (17 \div (1)/(6))) \div (5 + (1)/(4))\right\} \]

2. **Calculate the first part**:
\[ 120 \div 5 = 24 \]
Now divide by 4:
\[ 24 \div 4 = 6 \]

3. **Calculate the second part inside the brackets**:
- Start with \( 105 - 5 \times 3 + 2 \text{ of } (17 \div (1)/(6)) \).
- Calculate \( 5 \times 3 = 15 \).
- Now calculate \( 17 \div (1)/(6) = 17 \times 6 = 102 \).
- Thus, \( 2 \text{ of } 102 = 2 \times 102 = 204 \).
- Now substitute these values back:
\[ 105 - 15 + 204 = 105 - 15 + 204 = 294 \]

4. **Now divide by \( 5 + (1)/(4) \)**:
- Calculate \( 5 + (1)/(4) = 5 + 0.25 = 5.25 \).
- Now divide:
\[ 294 \div 5.25 = \frac{294}{5.25} = \frac{294 \times 100}{525} = \frac{29400}{525} = 56 \]

5. **Final Calculation**:
\[ 6 - 56 = -50 \]

### Final Answer:
The value of the expression is \(-50\).