Final answer:
When given that 60% of the cost price is equal to 40% of the selling price, after solving for the ratio of SP to CP, we find that the selling price is 150% of the cost price, indicating a 50% profit. Thus, none of the given options are correct; the answer is a 50% profit.
Step-by-step explanation:
Let's denote the cost price of the item as CP and the selling price as SP. According to the problem, 60% of the cost price is equal to 40% of the selling price, which can be represented as:
0.60 × CP = 0.40 × SP
By simplifying this equation, we can solve for the ratio of SP to CP:
SP/CP = (0.60/0.40) = 1.5
This means the selling price is 1.5 times the cost price, or in other words, SP = 150% of CP. The profit made on the item is the difference between the selling price and the cost price, which would be:
Profit = SP - CP
Since SP is 150% of CP, this means there is a 50% increase from the cost price to the selling price. Hence, the percentage of profit is 50%.
Therefore, none of the provided options A) 20% profit, B) 20% loss, C) 40% profit, D) 40% loss are correct. The correct answer would be a 50% profit.