Simple interest on a certain sum of money for 3 years at 10% per annum is half the compound interest on Rs 6000 for 2 years at 10% per annum. The sum placed on simple interest is

Sum for compound interest = Rs. 6000

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

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

= $$6000 [(1 + \frac{10}{100})^2 - 1]$$

= $$6000 [(\frac{11}{10})^2 - 1] = 6000 (\frac{121 - 100}{100})$$

= $$60 \times 21 = $$Rs. $$1260$$

=> Simple interest = $$\frac{1260}{2} = Rs. 630$$

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

Rate of interest = 10% and time period = 3 years

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

= $$\frac{x \times 10 \times 3}{100} = 630$$

=> $$x = \frac{630 \times 10}{3} = 210 \times 10 = Rs. 2100$$

=> Ans - (B)