A sum of Rs. 5,000 divided into two parts such that the simple interest on the first part for $$4\frac{1}{5}$$ years at $$6\frac{2}{3}\% $$  p.a. is double the simple interest on the second part for $$2\frac{3}{4}$$ years at 4% p.a. The ratio of the second part to the first part is:

$$\eqalign{ & {\text{S}}{\text{.}}{{\text{I}}_1} = 2 \times {\text{S}}{\text{.}}{{\text{I}}_2} \cr & \frac{{x \times 20 \times 21}}{{100 \times 3 \times 5}} = 2 \times \frac{{y \times 4 \times 11}}{{100 \times 4}} \cr & 28x = 22y \cr & x:y = 22:28 \cr & {\text{Ratio of second part of first part}} \cr & y:x = 28:22 = 14:11 \cr} $$