Simple interest on a certain sum of money for 3 years at 16% per annum is half the compound interest on Rs. 12000 for 2 years at 10% per annum. The sum placed on simple interest is

Sum for compound interest = Rs. 12000

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

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

= $$12000 [(1 + \frac{10}{100})^2 - 1]$$

= $$12000 [(\frac{11}{10})^2 - 1] = 12000 (\frac{121 - 100}{100})$$

= $$120 \times 21 = $$Rs. $$2520$$

=> Simple interest = $$\frac{2520}{2} = Rs. 1260$$

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

Rate of interest = 16% and time period = 3 years

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

= $$\frac{x \times 16 \times 3}{100} = 1260$$

=> $$x = \frac{1260 \times 25}{12} = 105 \times 25 = Rs. 2625$$