Discussion
The present worth of a certain bill due sometime hence is Rs.800 and true discount is Rs.36. The banker's discount is?
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.
\[ k = \frac{\text{TD}}{\text{PW}} = \frac{36}{800} = 0.045 \]
\[ A = \text{PW} + \text{TD} = 800 + 36 = \text{Rs. } 836 \]
\[ \text{BD} = A\,k = 836 \times 0.045 = \text{Rs. } 37.62 \]
Equivalently \( \text{BD} = \text{TD}(1+k) = 36 \times 1.045 = 37.62 \). The banker's gain is the 62 paise difference.
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