Discussion
If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Answer: D
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:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
First find the rate–time product from the original bill.
\[ \text{PW} = 110 - 10 = 100 \quad\Longrightarrow\quad 100 \times \frac{RT}{100} = 10 \quad\Longrightarrow\quad \frac{RT}{100} = 0.1 \]
Doubling the time doubles that product to 0.2, so for the same Rs. 110:
\[ \text{PW}' = \frac{110}{1.2} = 91.67 \]
\[ \text{TD}' = 110 - 91.67 = 18.33 \]
True discount does not double when the time doubles - the Rs. 20 option is exactly that trap. It grows more slowly because the present worth shrinks at the same time.
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