If the difference between the compound and simple interests on a certain sum of money for 3 years at 5% per annum is ₹15.25, find the sum. (C.P.O., 2006)
Answer
Answer (as printed):
Explanation
Let the sum be ₹x. Then, C.I. $=x\left(1+\frac{5}{100}\right)^{3}-x=\frac{9261}{8000}x-x=\frac{1261}{8000}x$. S.I. $=\left(\frac{x \times 5 \times 3}{100}\right)=\frac{3x}{20}$. ∴ (C.I.) − (S.I.) $=\left(\frac{1261}{8000}x-\frac{3x}{20}\right)=\frac{61x}{8000}$. So, $\frac{61x}{8000}=15.25$ $\Leftrightarrow x=\frac{15.25 \times 8000}{61}=2000$. Hence, required sum $=₹2000$.
Explanation as extracted from the printed page; notation may be imperfect.