Discussion
A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
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:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
The Rs. 3600 is not received today but in 2 years, so compare its present worth with the Rs. 3000 he spent.
\[ \text{PW} = \frac{3600}{1 + \dfrac{10 \times 2}{100}} = \frac{3600}{1.2} = 3000 \]
The present worth exactly equals the cost price, so
\[ \text{gain} = 3000 - 3000 = 0 \quad\Longrightarrow\quad 0\% \]
Comparing Rs. 3600 with Rs. 3000 directly suggests a 20% profit, but that ignores two years of waiting - which is precisely what true discount measures.
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