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If the expression $${\text{2}}\frac{1}{2}{\text{ of }}\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{3}{2}\left[ {\frac{2}{3} - \frac{1}{2}{\text{ of }}\frac{2}{3}} \right]$$        is simplified, we get -

A. $$\frac{1}{2}$$

B. $$\frac{7}{8}$$

C. $${\text{1}}\frac{5}{8}$$

D. $${\text{2}}\frac{3}{5}$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given expression,}} \cr & = \frac{5}{2}of\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{3}{2}\left[ {\frac{2}{3} - \frac{1}{3}} \right] \cr & = \frac{5}{2}of\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \left( {\frac{3}{2} \times \frac{1}{3}} \right) \cr & = \frac{{15}}{8} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{1}{2} \cr & = \frac{{15}}{8} \times \frac{1}{2} \times \frac{2}{3} + \frac{1}{2} \times 2 \cr & = \frac{5}{8} + 1 \cr & = \,1\frac{5}{8} \cr} $$

This Question Belongs to Arithmetic Ability >> Simplification

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