Question : Solve the following.
$\frac{24 \div \frac{3}{8} \text { of }(8+2 \times \overline{7-3})+\left[\frac{2}{11} \div \frac{4}{55}-\left\{\frac{5}{8}+\frac{6}{16}\right\}\right]}{32 \div \overline{15-7}+75 \div(6+15 \div 3+4)} $
Option 1: $\frac{23}{27}$
Option 2: $\frac{9}{2}$
Option 3: $\frac{11}{18}$
Option 4: $\frac{15}{19}$
Correct Answer: $\frac{11}{18}$
Solution :
$⇒\frac{24 \div \frac{3}{8} \text { of }(8+2 \times \overline{7-3})+\left[\frac{2}{11} \div \frac{4}{55}-\left\{\frac{5}{8}+\frac{6}{16}\right\}\right]}{32 \div \overline{15-7}+75 \div(6+15 \div 3+4)}$
First, we have to solve Vinculum,
$⇒\frac{24 \div \frac{3}{8} \text { of }(8+2 \times 4)+\left[\frac{2}{11} \div \frac{4}{55}-\left\{\frac{5}{8}+\frac{6}{16}\right\}\right]}{32 \div 8+75 \div(6+15 \div 3+4)}$
Now, we have to solve Brackets
$⇒\frac{24 \div \frac{3}{8} \text { of }(16)+\left[\frac{2}{11} \times \frac{55}{4}-\left\{\frac{10+6}{16}\right\}\right]}{32 \div 8+75 \div(6+5+4)}$
$⇒\frac{24 \div \frac{3}{8} \text { of }(16)+\left[\frac{5}{2}-\frac{16}{16}\right]}{32 \div 8+75 \div 15}$
$⇒\frac{24 \div \frac{3}{8} \text { of }16+\left[\frac{5}{2}-1\right]}{32 \div 8+75 \div 15}$
$⇒\frac{24 \div \frac{3}{8} \text { of }16+\frac{3}{2}}{32 \div 8+75 \div 15}$
Now, we have to solve Of
$⇒\frac{24 \div 6+\frac{3}{2}}{32 \div 8+75 \div 15}$
Now, We have to solve the Divide
$⇒\frac{4+\frac{3}{2}}{4+5}$
$⇒\frac{\frac{8+3}{2}}{9}$
$⇒\frac{11}{18}$
Hence, the correct answer is $\frac{11}{18}$.
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