Discussion
The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount.
Answer: B
Four quantities are related throughout this topic. Writing \( k = \dfrac{RT}{100} \):
\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]
The banker's discount is interest on the face value; the true discount is interest on the present worth; the banker's gain is the interest on the true discount.
\[ k = \frac{\text{TD}}{\text{PW}} = \frac{110}{1100} = 0.1 \]
\[ A = \text{PW} + \text{TD} = 1100 + 110 = \text{Rs. } 1210 \]
\[ \text{BD} = A\,k = 1210 \times 0.1 = \text{Rs. } 121 \]
The banker's gain is \( 121 - 110 = \text{Rs. } 11 \), which is also \( \text{TD} \times k = 110 \times 0.1 \) - a useful cross-check.
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