Discussion
I purchased a bike for Rs. 1056 in cash and sold it the same day for Rs. 1296, payable after 8 months. If the rate of interest is 12% per annum, what was my gain per cent?
Answer: C
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
The Rs. 1296 is payable after 8 months, so \( T = \dfrac{8}{12} = \dfrac{2}{3} \) year at 12%:
\[ \frac{RT}{100} = \frac{12 \times 2/3}{100} = 0.08 \]
\[ \text{PW} = \frac{1296}{1.08} = \text{Rs. } 1200 \]
\[ \text{gain} = 1200 - 1056 = \text{Rs. } 144 \]
\[ \text{gain}\% = \frac{144}{1056} \times 100 = 13.64\% \approx 13.6\% \]
Comparing Rs. 1296 with Rs. 1056 directly suggests 22.7% - the last distractor - but that ignores the eight months of waiting.
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