What is the value of the following expression?
​$$\frac{4}{7}×4 \frac{1}{2}÷5\frac{ 1}{3 }\ of \ 2 \frac{1}{2}-(7 \frac{7}{8}÷5 \frac{1}{9} of \ 9 \frac{9}{20})+\frac{1}{2 }$$​​

Correct option is A

Given:
​$$\frac{4}{7}×4 \frac{1}{2}÷5\frac{ 1}{3 }\ of \ 2 \frac{1}{2}-(7 \frac{7}{8}÷5 \frac{1}{9} of \ 9 \frac{9}{20})+\frac{1}{2 }$$​​
Solution:  

$$\begin{aligned}&\text{ } \frac{4}{7} \times 4 \frac{1}{2} \div 5 \frac{1}{3} \text{ of } 2 \frac{1}{2} - \left( 7 \frac{7}{8} \div 5 \frac{1}{9} \text{ of } 9 \frac{9}{20} \right) + \frac{1}{2} \\&= \frac{4}{7} \times \frac{9}{2} \div \frac{16}{3} \times \frac{5}{2} - \left( \frac{63}{8} \div \frac{46}{9} \times \frac{189}{20} \right) + \frac{1}{2} \\&= \frac{4}{7} \times \frac{9}{2} \times \frac{3}{40} - \left( \frac{63}{8} \times \frac{10}{483} \right) + \frac{1}{2} \\&= \frac{1}{7} \times \frac{9}{2} \times \frac{3}{10} - \left( \frac{21}{4} \times \frac{5}{161} \right) + \frac{1}{2} \\&= \frac{27}{140} - \frac{15}{92} + \frac{1}{2} \\&= \frac{621}{3220} - \frac{525}{3220} + \frac{1610}{3220} \\&= \frac{1706}{3220} = \frac{853}{1610}.\end{aligned}$$​