Question

The simple interest on a certain sum for 3 years is Rs. 1080 and the compound interest on the same sum at the same rate for 2 years is Rs. 741.60. Find :

1. The rate of interest.

2. The principal.

Answer 1

$$\begin{gathered} LetthesumisPandrateisr \\ SI=\frac{P\times r\times t}{100} \\ 1080=\frac{Pr3}{100}Pr=360,00P=\frac{36000}{r}---------(1)CI=A-Pso,A=CI\hspace{0.17em}+PCI+P=P(1+\frac{r}{100})2741.6=P[(1+\frac{r}{100})2-1]741.6=\frac{36000}{r}\{(1+\frac{r}{100}-1)(1+\frac{r}{100}+1)\}Onsolvingthiswegetr=6\%P=\frac{36000}{r}=Rs.6000 \end{gathered}$$