Question : What is the value of $\frac{\left(\frac{28}{9} \times \frac{42}{35}\right) \div\left(\frac{3}{25} \times \frac{5}{7} \div \frac{1}{21}\right)}{\left(\frac{14}{15} \div \frac{2}{75} \text { of } \frac{7}{5}\right) \times \frac{1}{75} \div \frac{4}{3}} ?$
Option 1: $\frac{222}{27}$
Option 2: $\frac{212}{27}$
Option 3: $\frac{244}{27}$
Option 4: $\frac{224}{27}$
Correct Answer: $\frac{224}{27}$
Solution :
$\frac{(\frac{28}{9} \times \frac{42}{35}) \div(\frac{3}{25} \times \frac{5}{7} \div \frac{1}{21})}{(\frac{14}{15} \div \frac{2}{75} \text { of }\frac{7}{5}) \times \frac{1}{75} \div \frac{4}{3}}$
= $\frac{(\frac{4}{3}×\frac{14}{5})÷(\frac{3}{25}×\frac{5}{7}×21)}{(\frac{14}{15}÷\frac{14}{375})×\frac{1}{75}×\frac{3}{4}}$
= $\frac{(\frac{4}{3}×\frac{14}{5})÷(\frac{3}{5}×3)}{(\frac{14}{15}×\frac{375}{14})×\frac{1}{75}×\frac{3}{4}}$
= $\frac{\frac{4}{3}×\frac{14}{5}×\frac{5}{9}}{25×\frac{1}{75}×\frac{3}{4}}$
= $\frac{56}{27}×4$
= $\frac{224}{27}$
Hence, the correct answer is $\frac{224}{27}$.
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