The value of $$\frac{1}{4} + \frac{{\left[ {{{\left( {20.35} \right)}^2} - {{\left( {8.35} \right)}^2}} \right] \times 0.0175}}{{{{\left( {1.05} \right)}^2} + \left( {1.05} \right)\left( {27.65} \right)}}{\text{is:}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{1}{4} + \frac{{\left[ {{{\left( {20.35} \right)}^2} - {{\left( {8.35} \right)}^2}} \right] \times 0.0175}}{{{{\left( {1.05} \right)}^2} + \left( {1.05} \right)\left( {27.65} \right)}} \cr & = \frac{1}{4} + \frac{{\left[ {\left( {20.35 + 8.35} \right)\left( {20.35 - 8.35} \right)} \right] \times 0.0175}}{{\left( {1.05} \right) + \left[ {1.05 + 27.65} \right]}} \cr & = \frac{1}{4} + \frac{{\left[ {\left( {28.70} \right)\left( {12} \right) \times 0.0175} \right]}}{{\left( {1.05} \right)\left[ {28.70} \right]}} \cr & = \frac{1}{4} + \frac{{12 \times 5}}{{300}} \cr & = \frac{1}{4} + \frac{1}{5} \cr & = \frac{9}{{20}} \cr} $$