Discussion

The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker’s discount?

Answer: A

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

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

\[ k = \frac{\text{TD}}{\text{PW}} = \frac{72}{1296} = \frac{1}{18} \]

\[ A = 1296 + 72 = \text{Rs. } 1368 \]

\[ \text{BD} = A\,k = \frac{1368}{18} = \text{Rs. } 76 \]

Equivalently \( \text{BD} = \text{TD}(1+k) = 72 \times \tfrac{19}{18} = 76 \), the banker's gain being the Rs. 4 difference.

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