If $${\text{A}} = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.2} \right)}^3} + {{\left( {0.3} \right)}^3} + 3\left( {0.005 + 0.016 + 0.027} \right) + 0.036}}{{{{\left( {0.1} \right)}^2} + {{\left( {0.2} \right)}^2} + {{\left( {0.3} \right)}^2} + 0.04 + 0.06 + 0.12}}$$            then the value of 60A is:

Solution(By Examveda Team)

$$\eqalign{ & {\text{A}} = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.2} \right)}^3} + {{\left( {0.3} \right)}^3} + 3\left( {0.005 + 0.016 + 0.027} \right) + 0.036}}{{{{\left( {0.1} \right)}^2} + {{\left( {0.2} \right)}^2} + {{\left( {0.3} \right)}^2} + 0.04 + 0.06 + 0.12}} \cr & {\text{A}} = \frac{{{{10}^{ - 3}}\left[ {{1^3} + {2^3} + {3^3} + 3\left( {5 + 16 + 27} \right) + 36} \right]}}{{{{10}^{ - 2}}\left[ {{1^2} + {2^2} + {3^2} + 4 + 6 + 12} \right]}} \cr & {\text{A}} = \frac{{1 + 8 + 27 + 144 + 36}}{{10 \times 36}} \cr & {\text{A}} = \frac{{216}}{{10 \times 36}} \cr & {\text{A}} = \frac{6}{{10}} \cr & {\text{Hence, 60A}} = 60 \times \frac{6}{{10}} = 36{\text{ Answer}} \cr} $$