Discussion
A shopkeeper wants to make some profit by selling sugar. Which of the following would maximize his profit?
A.Sell sugar at 10% profit
B.Use 900 g of weight instead of 1 kg
C.Mix 10% impurities in sugar and selling sugar at cost price
D.Increase the price by 5% and reduced weight by 5%
Answer: A
The answer is ii: using 900 g of weight instead of 1 kg gives the most profit.
The options number the four methods i to iv in the order printed. Compare the profit of each on the cost of the sugar actually handed over:
- i: a 10% profit.
- ii: the customer pays for 1000 g but gets 900 g, so the profit is \(\frac{100}{900}\), about 11.1%.
- iii: adding 10% impurities to the sugar and selling at cost: 1.1 kg is sold for the cost of 1.1 kg of sugar while only 1 kg is sugar, a profit of 10%.
- iv: 5% more price for 5% less weight: \(\frac{1.05}{0.95}\), about 10.5%.
So method ii alone gives the most. The trap is in ii: cheating on weight by 10% yields more than 10% profit, because the gain is measured on the smaller quantity actually sold.
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