Let Rs x invested at 10 % simple interest. Then Rs. (2000 - x) are invested at the rate of 15% simple interest

\( \Large \frac{x \times 10 \times 2}{100} + \frac{(2000 - x)\times 15 \times 2}{100} = 460 \)

= > \( \Large\frac{2x}{10} + \frac{3(2000 - x)}{10} = 460 \)

= > x = 1400

Thus, Rs.1400 are invested at the rate of 10% and Rs. 600 are invested at the rate of 15% simple interest.

Required ratio = 1400 / 600 = 7/3.