Discussion

The banker's discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:

Answer: A

Writing \( k = \dfrac{RT}{100} \), the four quantities are related by

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

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

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

Dividing one by the other:

\[ \frac{72}{60} = \frac{A}{A - 60} \quad\Longrightarrow\quad 72A - 4320 = 60A \]

\[ 12A = 4320 \quad\Longrightarrow\quad A = \text{Rs. } 360 \]

The standard shortcut is

\[ \text{Sum} = \frac{\text{BD} \times \text{TD}}{\text{BD} - \text{TD}} = \frac{72 \times 60}{12} = 360 \]

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