Rs. 12000 is divided into two parts such that simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for $$4\frac{1}{2}$$ years at 16% per annum. The ratio of the first part to the second part is = ?

Let two parts are P₁ and P₂ respectively
According to the question
$$\eqalign{ & \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr & 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr & \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr & {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr & {\text{Hence,}} \cr & {\text{Required ratio = 2 : 1}} \cr} $$