Discussion
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
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:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
The Rs. 2200 arrives a year late, so discount it back to today.
\[ \text{PW} = \frac{2200}{1 + \dfrac{10 \times 1}{100}} = \frac{2200}{1.1} = 2000 \]
\[ \text{gain} = 2000 - 1950 = \text{Rs. } 50 \]
Comparing 2200 with 1950 suggests a Rs. 250 profit, but Rs. 200 of that is merely compensation for waiting a year - only the remaining Rs. 50 is real gain.
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