An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The total interest obtained after 2 years from both the schemes together is Rs 2090. If both the schemes have 18% per annum interest rate, then what is the first year interest (in Rs) of simple interest scheme?

Let sum invested in both schemes = Rs. $$100x$$

Time period = 2 years and rate of interest in both schemes = 18%

Total interest from both schemes = $$(\frac{P\times R\times T}{100})+[P(1+\frac{R}{100})^T-P]$$

=> $$(\frac{100x\times 18\times 2}{100})+[100x(1+\frac{18}{100})^2-100x]=2090$$

=> $$(36x)+[100x(\frac{118}{100})^2-100x]=2090$$

=> $$36x+139.24x-100x=2090$$

=> $$75.24x=2090$$

=> $$x=\frac{2090}{75.24}=27.78$$

$$\therefore$$ Simple interest in 1st year = $$\frac{(100\times27.78)\times18\times1}{100}$$

= $$27.78\times18=500.04\approx Rs.$$ $$500$$

=> Ans - (B)