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 is:

Answer: C

Simple interest is reckoned on the amount, true discount on the present worth. Both use the same \( \dfrac{RT}{100} \), so

\[ \text{SI} = A \times \frac{RT}{100}, \qquad \text{TD} = \text{PW} \times \frac{RT}{100} = (A - \text{TD}) \times \frac{RT}{100} \]

Dividing one by the other:

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

\[ 85A - 6800 = 80A \quad\Longrightarrow\quad 5A = 6800 \quad\Longrightarrow\quad A = 1360 \]

The shortcut worth remembering is

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

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