A sum becomes Rs 1392 in 2 years and Rs 1488 in 3 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 2 years = Rs. 1392

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

=> $$100x+\frac{100x\times r\times2}{100}=1392$$

=> $$100x+2rx=1392$$

=> $$x(100+2r)=1392$$ -----------------(i)

Similarly, after 3 years, => => $$100x+\frac{100x\times r\times3}{100}=1488$$

=> $$x(100+3r)=1488$$ --------------(ii)

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

=> $$\frac{100+3r}{100+2r}=\frac{1488}{1392}$$

=> $$139200+4176r=148800+2976r$$

=> $$4176r-2976r=100(1488-1392)$$

=> $$1200r=100\times96$$

=> $$r=\frac{96}{12}=8\%$$

=> Ans - (A)