The value of ` (16 ""(2)/(3) div 10 ) - [ (8/3 xx 5/4 ) " of " 2/5 +(16)/(3 ) xx (11)/(8) - (1/4 div (1)/(28))]` is-

Options

A. 1
B. 5
C. 0
D. 10

Answer

To solve the expression \( (16 \times \frac{2}{3} \div 10) - \left[ \left(\frac{8}{3} \times \frac{5}{4}\right) \text{ of } \frac{2}{5} + \left(\frac{16}{3} \times \frac{11}{8}\right) - \left(\frac{1}{4} \div \frac{1}{28}\right) \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate \( 16 \times \frac{2}{3} \div 10 \)**:
- First, calculate \( 16 \times \frac{2}{3} \):
\[ 16 \times \frac{2}{3} = \frac{32}{3} \]
- Now divide by 10:
\[ \frac{32}{3} \div 10 = \frac{32}{3} \times \frac{1}{10} = \frac{32}{30} = \frac{16}{15} \]

2. **Calculate the expression inside the brackets**:
- **Calculate \( \frac{8}{3} \times \frac{5}{4} \)**:
\[ \frac{8}{3} \times \frac{5}{4} = \frac{40}{12} = \frac{10}{3} \]
- **Calculate \( \frac{10}{3} \text{ of } \frac{2}{5} \)**:
\[ \frac{10}{3} \times \frac{2}{5} = \frac{20}{15} = \frac{4}{3} \]
- **Calculate \( \frac{16}{3} \times \frac{11}{8} \)**:
\[ \frac{16}{3} \times \frac{11}{8} = \frac{176}{24} = \frac{22}{3} \]
- **Calculate \( \frac{1}{4} \div \frac{1}{28} \)**:
\[ \frac{1}{4} \div \frac{1}{28} = \frac{1}{4} \times 28 = 7 \]

3. **Combine the results inside the brackets**:
- Now substitute back into the brackets:
\[ \frac{4}{3} + \frac{22}{3} - 7 \]
- Convert \( 7 \) to a fraction with a denominator of 3:
\[ 7 = \frac{21}{3} \]
- Combine:
\[ \frac{4}{3} + \frac{22}{3} - \frac{21}{3} = \frac{4 + 22 - 21}{3} = \frac{5}{3} \]

4. **Final calculation**:
- Now substitute back into the original expression:
\[ \frac{16}{15} - \frac{5}{3} \]
- Convert \( \frac{5}{3} \) to a fraction with a denominator of 15:
\[ \frac{5}{3} = \frac{25}{15} \]
- Now perform the subtraction:
\[ \frac{16}{15} - \frac{25}{15} = \frac{16 - 25}{15} = \frac{-9}{15} = -\frac{3}{5} \]

### Final Answer:
The value of the expression is \( -\frac{3}{5} \).