Discussion
The true discount on a bill of Rs.540 is rs.90 . 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.
\[ \text{PW} = 540 - 90 = \text{Rs. } 450 \quad\Longrightarrow\quad k = \frac{\text{TD}}{\text{PW}} = \frac{90}{450} = 0.2 \]
\[ \text{BD} = A\,k = 540 \times 0.2 = \text{Rs. } 108 \]
The banker's discount always exceeds the true discount, here by \( 108 - 90 = \text{Rs. } 18 \), because it charges interest on the larger face value.
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