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
First recover the rate–time product from the original bill.
\[ \text{PW} = 110 - 10 = 100 \quad\Longrightarrow\quad 100k = 10 \quad\Longrightarrow\quad k = 0.1 \]
Doubling the time doubles \( k \) to 0.2, so for the same Rs. 110:
\[ \text{PW}' = \frac{110}{1.2} = 91.67 \quad\Longrightarrow\quad \text{TD}' = 110 - 91.67 = \text{Rs. } 18.33 \]
True discount does not double when the time doubles - the Rs. 20 option is exactly that assumption. It grows more slowly, because the present worth it is computed on shrinks at the same time.
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