Discussion
The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:
Answer: B
Write \( k = \dfrac{R \times 2}{100} \) for the rate–time product over the two years. Simple interest is charged on the full sum, true discount on the present worth:
\[ \text{SI} = 750\,k, \qquad \text{TD} = \frac{960\,k}{1+k} \]
Setting them equal and cancelling \( k \):
\[ 750(1+k) = 960 \quad\Longrightarrow\quad 1 + k = 1.28 \quad\Longrightarrow\quad k = 0.28 \]
\[ \frac{2R}{100} = 0.28 \quad\Longrightarrow\quad R = 14\% \]
Cancelling \( k \) from both sides is what makes the problem solvable in one line; the two years then divide out at the very end.
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