Question

The simple interest on a sum of money is $\dfrac{4}{9}$ of the principal and the number of years is equal to the rate percent per annum. The rate per annum is:
$
  {\text{A}}{\text{. }}5\% \\
  {\text{B}}{\text{. }}6\dfrac{2}{3}\% \\
  {\text{C}}{\text{. }}6\% \\
  {\text{D}}{\text{. }}7\dfrac{1}{5}\% \\
 $

Answer 1

Hint: Here we go through by the formula of simple interest that we study in the chapter of simple interest. i.e.$SI = \dfrac{{P \times R \times T}}{{100}}$ . By this formula we will be able to calculate the rate.

Complete step-by-step answer:
Here in the question the principal amount is not given.
So let the principle amount be Rs x.
And Rate of interest be R%.
Here in the question it is given that the number of years is equal to the rate percent per annum, i.e.
Time=R.
It is also given that the simple interest on a sum of money is $\dfrac{4}{9}$ of the principal. i.e.
Simple interest =$\dfrac{4}{9}{\text{ }}of{\text{ }}x = \dfrac{{4x}}{9}$
Now put these values in the formula of S.I i.e. $SI = \dfrac{{P \times R \times T}}{{100}}$we get,
$ \Rightarrow \dfrac{{4x}}{9} = \dfrac{{x \times R \times R}}{{100}}$ as the rate and the time are given equal in the question.
$
   \Rightarrow \dfrac{{4x}}{9} = \dfrac{{(x \times {R^2})}}{{100}} \\
   \Rightarrow \dfrac{4}{9} = \dfrac{{{R^2}}}{{100}} \\
   \Rightarrow {R^2} = 100 \times \dfrac{4}{9} \\
   \Rightarrow R = 10 \times \dfrac{2}{3} = \dfrac{{20}}{3} \\
 $
Therefore, the rate of interest is $\dfrac{{20}}{3}\% $ or $6\dfrac{2}{3}\% $.
Hence option B is the correct answer.

Note: - Whenever we face such a type of question, the key concept for solving the question is to first assume the principal amount because the principal amount is not given and then proceed with the question to find the S.I. Then by putting the formula of S.I we will get the terms which we need to find.