The value of $$\frac{{27 \times {{\left( {0.25} \right)}^3} + 125{{\left( {0.05} \right)}^3}}}{{{{\left( {0.75} \right)}^2} - 0.25 \times 0.5}}$$     is:

Solution (By Examveda Team)

$$\eqalign{ & \frac{{27 \times {{\left( {0.25} \right)}^3} + 125{{\left( {0.05} \right)}^3}}}{{{{\left( {0.75} \right)}^2} - 0.25 \times 0.5}} \cr & = \frac{{\frac{{27 \times 25 \times 25 \times 25}}{{1000000}} + \frac{{125 \times 5 \times 5 \times 5}}{{1000000}}}}{{\frac{{75 \times 75}}{{10000}} - \frac{{25 \times 5}}{{1000}}}} \cr & = \frac{{\frac{{27 \times 25 \times 25 \times 25}}{{1000}} + \frac{{125 \times 5 \times 5 \times 5}}{{1000}}}}{{\frac{{75 \times 75 - 25 \times 5 \times 10}}{{10}}}} \cr & = \frac{{\frac{{27}}{8} + \frac{1}{8}}}{{\frac{{45 - 10}}{{10}}}} \cr & = \frac{{280}}{{8 \times 35}} \cr & = 1 \cr} $$