Discussion

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

Answer: B

The present worth (PW) is what the sum is really worth today; the true discount (TD) is the interest that PW would earn over the remaining time:

\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]

Rearranging gives the standard relation

\[ \text{TD} = \frac{\text{Amount} \times \frac{RT}{100}}{1 + \frac{RT}{100}} \]

Here \( T = \dfrac{9}{12} = 0.75 \) year at 16%:

\[ \frac{RT}{100} = \frac{16 \times 0.75}{100} = 0.12 \]

\[ 189 = \frac{A \times 0.12}{1.12} \quad\Longrightarrow\quad A = \frac{189 \times 1.12}{0.12} = 1764 \]

As a check, PW = 1764 − 189 = 1575, and 12% of 1575 is indeed 189.

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