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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:

  • A.0%
  • B.5%
  • C.7.5%
  • D.10%

Answer: A

\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]

\[ \text{PW} = \frac{3600}{1 + \dfrac{10 \times 2}{100}} = \frac{3600}{1.2} = \text{Rs. } 3000 \]

The present worth exactly matches what he paid, so

\[ \text{gain} = 3000 - 3000 = 0 \quad\Longrightarrow\quad 0\% \]

The apparent Rs. 600 profit is exactly the interest the money would have earned over the two years, so in real terms he is no better off.

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