Discussion

The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum due is:

Answer: A

Simple interest is reckoned on the amount, true discount on the present worth, and both use the same rate–time product \( k \):

\[ \text{SI} = A\,k, \qquad \text{TD} = (A - \text{TD})\,k \]

\[ \frac{\text{SI}}{\text{TD}} = \frac{A}{A - \text{TD}} \quad\Longrightarrow\quad \frac{85}{80} = \frac{A}{A - 80} \]

\[ 85A - 6800 = 80A \quad\Longrightarrow\quad 5A = 6800 \quad\Longrightarrow\quad A = \text{Rs. } 1360 \]

The standard shortcut is

\[ \text{Sum} = \frac{\text{SI} \times \text{TD}}{\text{SI} - \text{TD}} = \frac{85 \times 80}{5} = 1360 \]

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