A sum of money invested at compound interest amounts to ₹4500 in 3 years and to ₹6750 in 6 years. The sum invested (in ₹) was:

Over each block of three years the money grows by the same factor, and that factor is 6750/4500 = 1.5. So the sum invested = 4500/1.5 = ₹3000. (Halving ₹4500 to ₹2250 assumes the interest is proportional to time — simple-interest thinking applied to a compound-interest sum.)