1. Stating the problem: An investor invested a total amount $T$ in two ventures with the same percentage return per year. From the total amount, $\frac{3}{10}T + 600$ was invested in the first venture. 2. The return from the first venture after one year was Rs 384, and the total return from both ventures was Rs 1120. 3. Let the common percentage return per year be $r$ (as a decimal). 4. The amount invested in the first venture is $\frac{3}{10}T + 600$, so the return from the first venture is: $$ r \times \left( \frac{3}{10}T + 600 \right) = 384 $$ 5. The remaining amount invested in the second venture is: $$ T - \left( \frac{3}{10}T + 600 \right) = \frac{7}{10}T - 600 $$ 6. The return from the second venture is: $$ r \times \left( \frac{7}{10}T - 600 \right) $$ 7. Total return is given as Rs 1120, so: $$ r \times \left( \frac{3}{10}T + 600 \right) + r \times \left( \frac{7}{10}T - 600 \right) = 1120 $$ 8. Factor out $r$: $$ r \times \left[ \left( \frac{3}{10}T + 600 \right) + \left( \frac{7}{10}T - 600 \right) \right] = 1120 $$ 9. Simplify the expression inside the brackets: $$ \frac{3}{10}T + 600 + \frac{7}{10}T - 600 = \frac{3}{10}T + \frac{7}{10}T = T $$ 10. So the equation simplifies to: $$ r \times T = 1120 $$ 11. From step 4, solve for $r$: $$ r = \frac{384}{\frac{3}{10}T + 600} $$ 12. Substitute this value of $r$ into the equation from step 10: $$ \frac{384}{\frac{3}{10}T + 600} \times T = 1120 $$ 13. Multiply both sides by $\frac{3}{10}T + 600$: $$ 384 T = 1120 \times \left( \frac{3}{10}T + 600 \right) $$ 14. Expand the right side: $$ 384 T = 1120 \times \frac{3}{10}T + 1120 \times 600 $$ $$ 384 T = 336 T + 672000 $$ 15. Bring all terms to one side: $$ 384 T - 336 T = 672000 $$ $$ 48 T = 672000 $$ 16. Solve for $T$: $$ T = \frac{672000}{48} = 14000 $$ 17. The total amount invested $T$ is Rs 14000, which is not in the options given. 18. Check carefully if there is a mistake in interpreting the problem. 19. The problem states the amount invested in one venture is $\frac{3}{10}$ of total amount plus Rs 600, returns Rs 384; total return Rs 1120. 20. If this is correct, the amount invested total is Rs 14000. 21. Since Rs 14000 is not among the options, confirm all steps. The computation is correct with the given data. Final answer: The total amount invested is Rs 14000.