The difference between simple and compound interest on a sum of money at 20% per annum for 3 years is Rs. 48. What is the sum?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{sum}}\,{\text{is}}\,P. \cr & {\text{The}}\,{\text{difference}}\,{\text{between}}\,{\text{compound}}\,{\text{interest}}\,{\text{and}} \cr & \,{\text{simple}}\,{\text{interest}}\,{\text{over}}\,{\text{three}}\,{\text{years}}\,{\text{is}}\,{\text{given}}\,{\text{by}} \cr & = P\left( {\frac{r}{{100}}} \right)2 \times \left\{ {\left( {\frac{r}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \left( {\frac{{20}}{{100}}} \right)2 \times \left\{ {\left( {\frac{{20}}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \frac{4}{{100}} \times \frac{{16}}{5} \cr & 48 = P \times \frac{{64}}{{500}} \cr & {\text{Or}},\,64P = 48 \times 500 \cr & {\text{Hence}},\,P = Rs.\,375 \cr} $$