Discussion

The present worth of a sum due sometimes hence is Rs.5760 and the baker’s gain is Rs.10. What is the true discount?

Answer: D

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

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

Neither the rate nor the time is given, so use the form that needs neither:

\[ \text{BG} = \frac{\text{TD}^{2}}{\text{PW}} \]

\[ 10 = \frac{\text{TD}^{2}}{5760} \quad\Longrightarrow\quad \text{TD}^{2} = 57{,}600 \]

\[ \text{TD} = \sqrt{57600} = \text{Rs. } 240 \]

The identity follows from \( \text{BG} = \text{TD}\,k \) and \( \text{TD} = \text{PW}\,k \): eliminating \( k \) between them gives it directly.

No comment is present. Be the first to comment.

Loading…