Discussion
The simple interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810 for the same time and at the same rate. The rate of interest per annum is:
Answer: A
Write \( k = \dfrac{R \times 2}{100} \). Simple interest is on the full sum; true discount is on the present worth:
\[ \text{SI} = 750\,k, \qquad \text{TD} = \frac{810\,k}{1+k} \]
Setting them equal and cancelling \( k \):
\[ 750(1+k) = 810 \quad\Longrightarrow\quad 1+k = 1.08 \quad\Longrightarrow\quad k = 0.08 \]
\[ \frac{2R}{100} = 0.08 \quad\Longrightarrow\quad R = 4\% \]
The two years enter only at the last step; everything before it is independent of the period.
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