A certain sum amounts to ₹11760 in $$2\frac{1}{2}$$ years at 9% p.a. simple interest. What will be the simple interest on the same sum for $$4\frac{2}{5}$$ years at 15% p.a?

Let the sum of money be Rs. $$100x$$

Rate of interest = $$r=9\%$$ and time period = $$t=\frac{5}{2}$$ years

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

=> $$100x+(\frac{100x\times5\times9}{2\times100})=11760$$

=> $$100x+22.5x=122.5x=11760$$

=> $$x=\frac{11760}{122.5}=96$$ --------------------(i)

Thus, simple interest after $$t'=\frac{22}{5}$$ years and $$r'=15\%$$

= $$\frac{100x\times22\times15}{5\times100}$$

= $$96\times66=Rs.$$ $$6336$$

=> Ans - (A)