​$$\text{Simplify: } \left[ \frac{1}{5} \text{ of } (5 \times 7 - 5) + 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - \left\{ 21 \div 3 + (2 - 3) \right\} + 5 \right]$$​​

Correct option is A

Given:

​$$\left[ \frac{1}{5} \text{ of } (5 \times 7 - 5) + 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - \left\{ 21 \div 3 + (2 - 3) \right\} + 5 \right]$$

Concept Used:

​$$\begin{array}{|l|l|}\hline\textbf{Operation preference wise} & \textbf{Symbol} \\\hline\text{Brackets} & [\,], \{\,\}, (\,) \\\hline\text{Orders, of} & ^x \, (\text{power}), \, \sqrt{} \, (\text{root}), \, \text{of} \\\hline\text{Division} & \div \\\hline\text{Multiplication} & \times \\\hline\text{Addition} & + \\\hline\text{Subtraction} & - \\\hline\end{array}$$

Solution:

$$\left[ \frac{1}{5} \text{ of } (5 \times 7 - 5) + 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - \left\{ 21 \div 3 + (2 - 3) \right\} + 5 \right]$$

=$$\left[ \frac{1}{5} \text{ of } (35 - 5) + 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - \left\{ 21 \div 3 -1 \right\} + 5 \right]$$

=$$\left[ \frac{1}{5} \text{ of } 30+ 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - \left\{7 -1 \right\} + 5 \right]$$

=$$\left[ 6+ 20 \div 5 \right] \div \left[ \frac{0.27}{0.03} - 6+ 5 \right]$$

=$$\left[ 6+ 4 \right] \div \left[ 9 - 6+ 5 \right]$$

=$$10 \div 8 = 1.25$$​