Discussion

The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 360. The banker’s discount is:

Answer: A

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

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

With \( k = \dfrac{12 \times 3}{100} = 0.36 \):

\[ \text{TD} = \frac{\text{BG}}{k} = \frac{360}{0.36} = \text{Rs. } 1000 \]

\[ \text{BD} = \text{TD} + \text{BG} = 1000 + 360 = \text{Rs. } 1360 \]

The banker's discount always exceeds the true discount by exactly the banker's gain.

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