Solution:
$$\eqalign{ 225 - \left[ {42 - \left\{ {25 - \left( {18 - \overline {18 + 13} } \right)} \right\}} \right] \cr = 225 - \left[ {42 - \left\{ {25 - \left( {18 - 18 - 13} \right)} \right\}} \right] \cr = 225 - \left[ {42 - \left\{ {25 + 13} \right\}} \right] \cr = 225 - \left[ {42 - 38} \right] \cr = 221 \cr} $$

Solution:
$$\eqalign{ \frac{{24 \div \frac{3}{8}{\text{of}}\left( {8 + 2 \times \overline {7 - 3} } \right) + \left[ {\frac{2}{{11}} \div \frac{4}{{55}} - \left\{ {\frac{5}{8} + \frac{6}{{16}}} \right\}} \right]}}{{32 \div \overline {15 - 7} + 75 \div \left( {6 + 15 \div 3 + 4} \right)}} \cr = \frac{{\left[ {24 \div \frac{3}{8}{\text{of}}\left( {8 + 2 \times 4} \right) + \left( {\frac{2}{{11}} \times \frac{{55}}{4} - \left\{ {\frac{{16}}{{16}}} \right\}} \right)} \right]}}{{32 \div 8 + 75 \div \left( {6 + 5 + 4} \right)}} \cr = \frac{{\left[ {24 \div 6 + \left( {\frac{5}{2} - 1} \right)} \right]}}{{\left[ {4 + 75 \div 15} \right]}} \cr = \frac{{\left[ {4 + \frac{3}{2}} \right]}}{{\left[ {4 + 5} \right]}} \cr = \frac{{\left[ {\frac{{11}}{2}} \right]}}{9} \cr = \frac{{11}}{{18}} \cr} $$

Solution:
$$\eqalign{ \frac{{9 \div \frac{3}{7}{\text{ of }}\left( {9 + 6 \times \overline {4 - 2} } \right) + \left[ {\frac{1}{5} \div \frac{7}{{25}} - \left\{ {\frac{5}{8} + \frac{6}{{16}}} \right\}} \right]}}{{24 \div \overline {16 - 10} + 36 \div \left( {5 + 20 \div 4 - 1} \right)}} \cr = \frac{{9 \div \frac{3}{7}{\text{ of }}\left( {9 + 6 \times 2} \right) + \left[ {\frac{1}{5} \times \frac{{25}}{7} - \left\{ {\frac{{10 + 6}}{{16}}} \right\}} \right]}}{{24 \div 6 + 36 \div \left( {5 + 5 - 1} \right)}} \cr = \frac{{9 \div \frac{3}{7}{\text{ of }}\left( {21} \right) + \left[ {\frac{5}{7} - 1} \right]}}{{4 + 36 \div 9}} \cr = \frac{{9 + \frac{{63}}{7} + \left( {\frac{{ - 2}}{7}} \right)}}{{4 + 4}} \cr = \frac{{1 - \frac{2}{7}}}{8} \cr = \frac{{\frac{5}{7}}}{8} \cr = \frac{5}{{56}} \cr} $$

Solution:
Given expression,
$$\left[ {\left( {x + \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}} - x.\frac{1}{x}} \right)} \right]$$     $$\left[ {\left( {x - \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}} + x.\frac{1}{x}} \right)} \right]$$
$$\eqalign{ = \left( {{x^3} + \frac{1}{{{x^3}}}} \right)\left( {{x^3} - \frac{1}{{{x^3}}}} \right) \cr = {x^6} - \frac{1}{{{x^6}}} \cr} $$

Solution:
$$\eqalign{ {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{number}}\,{\text{of}}\,{\text{shots}}\,{\text{be}}\,x. \cr {\text{Then,}}\,{\text{Shots}}\,{\text{fired}}\,{\text{by}}\,{\text{A}} = \frac{5}{8}x \cr {\text{Shots}}\,{\text{fired}}\,{\text{by}}\,{\text{B}} = \frac{3}{8}x \cr {\text{Killing}}\,{\text{shots}}\,{\text{by}}\,{\text{A}} \cr = \frac{1}{3}{\text{of}}\frac{5}{8}x = \frac{5}{{24}}x \cr {\text{Shots}}\,{\text{missed}}\,{\text{by}}\,{\text{B}} \cr = \frac{1}{2}{\text{of}}\,\frac{3}{8}x = \frac{3}{{16}}x \cr \therefore \frac{{3x}}{{16}} = 27\,{\text{or}}\,x = {\frac{{27 \times 16}}{3}} = 144 \cr {\text{Birds}}\,{\text{killed}}\,{\text{by}}\,{\text{A}} \cr = \frac{{5x}}{{24}} = {\frac{5}{{24}} \times 144} = 30 \cr} $$

Solution:
Given Expression
128.43 + 30.21 + ? = 173
⇒ ? = 173 - 128.43 - 30.21
⇒ ? = 173 - 158.64
⇒ ? = 14.36

Solution:
$$\eqalign{ {\text{According to question,}} \cr \sqrt {400} + \sqrt {0.0400} + \sqrt {0.000004} \cr \Rightarrow 20 + 0.2 + 0.002 \cr \Rightarrow 20.202 \cr} $$