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Question:

9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + 9 ÷ 4)}] = ?

Explanation:

Given: 9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + 9 ÷ 4)}]

= $\frac{9}{5+{\displaystyle \frac{7}{9+{\displaystyle \frac{9}{9+{\displaystyle \frac{9}{4}}}}}}}$

= $\frac{9}{5+{\displaystyle \frac{7}{9+{\displaystyle \frac{36}{45}}}}}$ = $\frac{9}{5+{\displaystyle \frac{7}{9+{\displaystyle \frac{4}{5}}}}}$

= $\frac{9}{5+{\displaystyle \frac{35}{49}}}$ = $\frac{9}{5+{\displaystyle \frac{5}{7}}}$

= $\frac{63}{40}$

Hence, option (b).