Mathematical Puzzle: Selling Candies to Earn a 50% Profit

Seemingly simple, this problem challenges our understanding of cost price, selling price, and profit. The task is to determine how many candies must be sold for a dollar to achieve a 50% profit margin, after purchasing candies at a cost that seems deceptively straightforward.

Solving the Puzzle Step-by-Step

To break this problem down, we'll start by identifying the cost price (CP) of the candies, then determine the selling price (SP) required to achieve a 50% profit, and finally, calculate the number of candies that can be sold for a dollar to realize that profit.

Cost Price Calculation

The man bought candies at a rate of 3 for a dollar. Therefore, the cost price of one candy is:

CP of one candy $frac{1}{3}$ ≈ $0.3333

Selling Price for 50% Profit

To earn a 50% profit, the selling price must be 1.5 times the cost price.

SP CP × 1.5 $frac{1}{3} × 1.5 frac{1.5}{3} frac{1}{2} $0.50

Calculating the Number of Candies Sold for a Dollar

Given that the selling price of each candy is $0.50, the number of candies he can sell for a dollar is:

Number of candies $frac{1}{0.5} 2$

So, to achieve a 50% profit, the man must sell 2 candies for a dollar.

Alternative Perspectives

However, there is a common critique that argues that the man cannot achieve a 50% profit selling candies at this rate. This critique is based on a misunderstanding of the problem. Let's consider the cost price per candy as a third of a dollar (i.e., $0.33) to illustrate the correct approach:

Re-examining the Selling Price for 50% Profit

To earn a 50% profit, the selling price per candy must be $0.33 $0.165 $0.495. However, this approach still leads us to the same conclusion that to sell for 1.5 times the cost, we need to sell each candy for $0.50.

Therefore, the revised selling price is still $0.50, and the number of candies sold for a dollar remains 2.

Conclusion

The correct answer is that the man must sell 2 candies for a dollar to earn a 50% profit. This logic holds true based on the given conditions, and it is a practical application of understanding cost, selling price, and profit margins.