Simple interest on a certain sum of money for 3 years at 18% per annum is half the compound interest on Rs. 9000 for 2 years at 10% per annum. The sum placed on simple interest is:

Sum for compound interest = Rs. 9000

Rate of interest = 10% and time period = 2 years

Compound interest = $$P [(1 + \frac{R}{100})^T - 1]$$

= $$9000 [(1 + \frac{10}{100})^2 - 1]$$

= $$9000 [(\frac{11}{10})^2 - 1] = 9000 (\frac{121 - 100}{100})$$

= $$90 \times 21 = $$Rs. $$1890$$

=> Simple interest = $$\frac{1890}{2} = Rs. 945$$

Let sum under simple interest = $$Rs. x$$

Rate of interest = 18% and time period = 3 years

Simple interest = $$\frac{P \times R \times T}{100}$$

= $$\frac{x \times 18 \times 3}{100} = 945$$

=> $$x = \frac{945 \times 100}{54} = 100 \times 17.5 = Rs. 1750$$

=> Ans - (C)