Discussion

The banker’s discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?

Answer: A

Writing \( k = \dfrac{RT}{100} \),

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]

Both discounts use the same \( k \), one on the amount and one on the present worth:

\[ \frac{\text{BD}}{\text{TD}} = \frac{A}{A - \text{TD}} \quad\Longrightarrow\quad \frac{36}{30} = \frac{A}{A - 30} \]

\[ 36A - 1080 = 30A \quad\Longrightarrow\quad 6A = 1080 \]

\[ A = \text{Rs. } 180 \]

The shortcut is

\[ \text{Sum} = \frac{\text{BD} \times \text{TD}}{\text{BD} - \text{TD}} = \frac{36 \times 30}{6} = 180 \]

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