Answer: Option A
$$\eqalign{
& {\text{Let the first part = Rs}}{\text{. }}x \cr
& \therefore {\text{Hence second part}} \cr
& {\text{ = Rs}}{\text{. }}\left( {12000 - x} \right) \cr
& {\text{According to the question,}} \cr
& \Rightarrow \frac{{x \times 12 \times 3}}{{100}} = \frac{{\left( {12000 - x} \right) \times 9 \times 16}}{{2 \times 100}} \cr
& \Rightarrow 36x = 72\left( {12000 - x} \right) \cr
& \Rightarrow x = 24000 - 2x \cr
& \Rightarrow 3x = 24000 \cr
& \Rightarrow x = {\text{Rs}}{\text{. 8000}} \cr
& {{\text{1}}^{{\text{st}}}}{\text{ part = Rs}}{\text{. 8000}} \cr
& {{\text{2}}^{{\text{nd}}}}{\text{ part}} \cr
& {\text{ = Rs}}{\text{. }}\left( {12000 - 8000} \right) \cr
& = {\text{Rs}}{\text{. 4000 }} \cr
& {\text{Hence maximum part}} \cr
& {\text{ = Rs}}{\text{. 8000}} \cr} $$
Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let two parts P1 and P2 respectively
According to the question,
$$\eqalign{
& \Rightarrow {{\text{P}}_1} \times \frac{{36}}{{100}} \times 1 = {{\text{P}}_2} \times \frac{9}{2} \times \frac{{16}}{{100}} \times 1 \cr
& \Rightarrow {{\text{P}}_1} \times 4 = 8{{\text{P}}_2} \cr
& \Rightarrow \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{2}{1} \cr
& \Rightarrow {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr
& {\text{Hence greater part}} \cr
& {\text{ = }}\frac{{12000}}{{\left( {2 + 1} \right)}} \times 2 \cr
& = {\text{Rs}}{\text{. }}8000 \cr} $$