Question

The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{CI}-\mathrm{SI}=\mathrm{Rs}283.50 \\ \mathrm{R}=15\% \\ \mathrm{n}=3\mathrm{years} \\ \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{Rs}\mathrm{x}. \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{A}=\mathrm{P}(1+\frac{\mathrm{R}}{100}{)}^{\mathrm{n}} \\ =\mathrm{P}(1+\frac{\mathrm{R}}{100}{)}^{\mathrm{n}} \\ =\mathrm{x}(1+\frac{15}{100}{)}^3 \\ =\mathrm{x}{\left(1.15\right)}^3...(1) \\ \mathrm{Also}, \\ \mathrm{SI}=\frac{\mathrm{PRT}}{100}=\frac{\mathrm{x}\left(15\right)\left(3\right)}{100}=0.45\mathrm{x} \\ \mathrm{A}=\mathrm{SI}+\mathrm{P}=1.45\mathrm{x}...(2) \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{x}{\left(1.15\right)}^3-1.45\mathrm{x}=283.50[\mathrm{From}\left(1\right)\mathrm{and}\left(2\right)] \\ 1.523\mathrm{x}-1.45\mathrm{x}=283.50 \\ 0.070875\mathrm{x}=283.50 \\ \mathrm{x}=\frac{283.50}{0.070875} \\ =4,000 \\ \mathrm{Thus},\mathrm{the}\mathrm{sum}\mathrm{is}\mathrm{Rs}4,000. \end{gathered}$$