Discussion
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The persent worth is?
Answer: C
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.
Here \( k = \dfrac{10 \times 2}{100} = 0.2 \).
\[ \text{BG} = \text{TD} \times k \quad\Longrightarrow\quad \text{TD} = \frac{24}{0.2} = \text{Rs. } 120 \]
\[ \text{TD} = \text{PW} \times k \quad\Longrightarrow\quad \text{PW} = \frac{120}{0.2} = \text{Rs. } 600 \]
The chain runs BG → TD → PW, dividing by \( k \) at each step. Stopping one step early leaves Rs. 120, and the face value would be Rs. 720.
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