Correct Answer: $\frac{9155}{2208}$

Solution : Given expression,
$\frac{5}{12} \times \frac{7}{12} \div\left(\frac{1}{75}+\frac{5}{12}\right.$ of $\left.\frac{36}{25}\right)+\frac{4}{5} \times \frac{75}{16}$
Using the BODMAS Rule,
B – Brackets, O – Of, D – Division, M – Multiplication A – Addition, and S – Subtraction
= $\frac{5}{12}\times\frac{7}{12}\div(\frac{1}{75}+\frac{5}{12}\times\frac{36}{25})+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5}{12}\times\frac{7}{12}\div(\frac{1}{75}+\frac{5\times3}{25})+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5}{12}\times\frac{7}{12}\div(\frac{1}{75}+\frac{15}{25})+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5}{12}\times\frac{7}{12}\div(\frac{1+45}{75})+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5}{12}\times\frac{7}{12}\div\frac{46}{75}+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5}{12}\times\frac{7}{12}\times\frac{75}{46}+\frac{4}{5}\times\frac{75}{16}$
= $\frac{5\times7\times25}{4\times12\times46}+\frac{15}{4}$
= $\frac{875}{2208}+\frac{15}{4}$
= $\frac{875+552\times15}{2208}$
= $\frac{875+8280}{2208}$
= $\frac{9155}{2208}$
Hence, the correct answer is $\frac{9155}{2208}$.