A shopkeeper sold \(\frac{2}{3}\) of his stock of rice at a profit of 5% and the remaining stock at a loss of 2%. If his total profit was ₹1000, then the cost price of the whole stock of rice is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹37,500
The profit on two-thirds of the stock minus the loss on the other third is the net profit of ₹1000; each is a percentage of the cost of its part.
Assuming the cost of the whole stock to be ₹\(C\):
Profit on \(\frac{2}{3}\) at 5%: \(\displaystyle\frac{2C}{3}\times\frac{5}{100}=\frac{C}{30}\)
Loss on \(\frac{1}{3}\) at 2%: \(\displaystyle\frac{C}{3}\times\frac{2}{100}=\frac{C}{150}\)
Net profit: \(\displaystyle\frac{C}{30}-\frac{C}{150}=\frac{4C}{150}=\frac{2C}{75}\)
\(\displaystyle\frac{2C}{75}=1000\), so \(C=37500\)
Shortcut:
Profit per cent on the whole stock: \(\displaystyle\frac{2}{3}\times5-\frac{1}{3}\times2=\frac{8}{3}\%\)
Cost \(\displaystyle=1000\times\frac{300}{8}=37500\)