Discussion

Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:

Answer: A

A 2% gain on Rs. 600 means the sale must be worth

\[ 600 \times 1.02 = \text{Rs. } 612 \text{ in today's money} \]

So Rs. 688.50 due in 9 months has a present worth of Rs. 612:

\[ 612\left(1 + \frac{R \times 0.75}{100}\right) = 688.50 \]

\[ 1 + 0.0075R = \frac{688.50}{612} = 1.125 \]

\[ 0.0075R = 0.125 \quad\Longrightarrow\quad R = \frac{50}{3} = 16\tfrac{2}{3}\% \]

The gain is reckoned on the present worth, not on the credit price - comparing 688.50 with 600 directly would suggest a 14.75% profit.

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