Question : What is the value of $\frac{\frac{5}{3} \text { of } \frac{1}{4} \times \frac{24}{5}-\frac{1}{5} \text { of } \frac{25}{8} \times \frac{24}{5}}{\frac{5}{12} \text { of } \frac{3}{4} \times \frac{4}{3}+\frac{3}{4} \text { of } \frac{12}{5} \times \frac{5}{6}}$?
Option 1: $-\frac{24}{23}$
Option 2: $-\frac{12}{23}$
Option 3: $-\frac{25}{46}$
Option 4: $-\frac{28}{23}$
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Correct Answer: $-\frac{12}{23}$
Solution :
$\frac{\frac{5}{3} \text { of } \frac{1}{4} \times \frac{24}{5}-\frac{1}{5} \text { of } \frac{25}{8} \times \frac{24}{5}}{\frac{5}{12} \text { of } \frac{3}{4} \times \frac{4}{3}+\frac{3}{4} \text { of } \frac{12}{5} \times \frac{5}{6}}$
$=\frac{\frac{5}{12}\times\frac{24}{5}-\frac{25}{40}\times\frac{24}{5}}{\frac{15}{48}\times\frac{4}{3}+\frac{36}{20}\times \frac{5}{6}}$
$=\frac{2-3}{\frac{5}{12}+\frac{3}{2}}$
$=\frac{-1}{\frac{5+18}{12}}$
$=\frac{-12}{23}$
Hence, the correct answer is $\frac{-12}{23}$.
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