The simple interest on a sum of money is 80% of the sum. The number of years for which the money was lent is \(\frac{4}{5}\) of the numerical value of the rate per cent per annum. What is the rate per cent per annum?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10%
Simple interest as a percentage of the sum is rate × time. Writing the time in terms of the rate leaves one unknown.
Let the rate be \(R\%\) per annum; time \(\displaystyle =\frac{4R}{5}\) years
\(\displaystyle R\times\frac{4R}{5}=80\)
\(R^{2}=100\), and the rate is positive, so \(R=10\)
The rate is 10% per annum (for 8 years, giving \(10\times8=80\%\) of the sum).