Question: The simple interest on a sum of money is $ \frac{1}{9} $ of the principal and the number of years is equal to rate per cent per annum. The rate per annum is
Options:
A) $ 3 $ %
B) $ \frac{1}{3} $ %
C) $ 3\frac{1}{3} $ %
D) $ \frac{3}{10} $ %
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \frac{Simpleinterest}{Principal}=\frac{1}{9} $
If the annual rate of interest is r%, then
$ Rate=\frac{SI\times 100}{Principal\times Time} $
$ \Rightarrow $ $ r=\frac{1}{9}\times \frac{100}{r} $ $ [\because t=r] $
$ \Rightarrow $ $ r^{2}=\frac{100}{9} $
$ \Rightarrow $ $ r=\sqrt{\frac{100}{9}}=\frac{10}{3}=3\frac{1}{3} $ %