A sum becomes Rs 2286 in 3 years and Rs 2448 in 4 years at simple interest. What is the rate (in percentage) of interest per annum?

Let sum = Rs. $$100x$$ and rate of interest = $$r\%$$

Amount after 3 years = Rs. 2286

=> Amount under simple interest = $$P+\frac{P\times R\times T}{100}$$

=> $$100x+\frac{100x\times r\times3}{100}=2286$$

=> $$100x+3rx=2286$$

=> $$x(100+3r)=2286$$ -----------------(i)

Similarly, after 4 years, => => $$100x+\frac{100x\times r\times4}{100}=2448$$

=> $$x(100+4r)=2448$$ --------------(ii)

Dividing equation (ii) by (i), we get :

=> $$\frac{100+4r}{100+3r}=\frac{2448}{2286}$$

=> $$228600+9144r=244800+7344r$$

=> $$9144r-7344r=100(2448-2286)$$

=> $$1800r=100\times162$$

=> $$r=\frac{162}{18}=9\%$$

=> Ans - (B)