Discussion
The true discount on a certain sum of money due 3 year hence is Rs.100 and the S.I. on the same sum for the same time and at the same rate is Rs.120. Find the sum and the rate percent.
Answer: A
Simple interest is charged on the whole sum, true discount only on the present worth, so
\[ \frac{\text{SI}}{\text{TD}} = \frac{A}{A - \text{TD}} \quad\Longrightarrow\quad \frac{120}{100} = \frac{A}{A - 100} \]
\[ 120A - 12000 = 100A \quad\Longrightarrow\quad A = \text{Rs. } 600 \]
Now use the simple-interest formula on that sum over 3 years:
\[ 120 = \frac{600 \times R \times 3}{100} = 18R \]
\[ R = \frac{120}{18} = \frac{20}{3} = 6\tfrac{2}{3}\% \]
The present worth is \( 600 - 100 = \text{Rs. } 500 \), and 20% of 500 is indeed Rs. 100 - a useful check on both answers at once.
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