Discussion

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:

Answer: A

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:

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

True discount is simple interest on the present worth, so start there:

\[ \frac{RT}{100} = \frac{14 \times 2}{100} = 0.28 \]

\[ \text{TD} = \text{PW} \times 0.28 \quad\Longrightarrow\quad 168 = 0.28\,\text{PW} \quad\Longrightarrow\quad \text{PW} = 600 \]

\[ \text{Sum due} = \text{PW} + \text{TD} = 600 + 168 = \text{Rs. } 768 \]

Dividing 168 by 0.28 gives the present worth, not the answer - the discount still has to be added back to reach the sum due.

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