Discussion
Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
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:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
\[ \text{PW} = 260 - 20 = 240 \quad\Longrightarrow\quad 240 \times \frac{RT}{100} = 20 \quad\Longrightarrow\quad \frac{RT}{100} = \frac{1}{12} \]
Halving the time halves that product to \( \dfrac{1}{24} \), so for the same Rs. 260:
\[ \text{PW}' = \frac{260}{1 + \frac{1}{24}} = \frac{260 \times 24}{25} = 249.60 \]
\[ \text{TD}' = 260 - 249.60 = \text{Rs. } 10.40 \]
Halving the time does not simply halve the discount to Rs. 10 - that is the first distractor, and it is slightly too small.
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