The simple interest of an amount is \(\frac{16}{25}\) of the principal. Find the rate of interest per annum, if the time and interest rate both are numerically equal.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8%
Simple interest is \(\displaystyle SI=\frac{P\times R\times T}{100}\). Since the rate and the time are the same number, \(R\times T=R^{2}\).
\(\displaystyle \frac{P\times R^{2}}{100}=\frac{16}{25}P\)
\(\displaystyle R^{2}=\frac{16\times100}{25}=64\)
\(R=8\), so the rate is 8% per annum (for 8 years)