Final answer:
The gain in percentage is 66.67% when the cost price of 20 oranges is equal to the selling price of 12 oranges. This is calculated by finding the ratio of gain per orange to the cost price of one orange and converting this ratio into a percentage.
Step-by-step explanation:
If the cost price of 20 oranges is equal to the selling price of 12 oranges, we are dealing with a profit calculation scenario. To determine the gain in percentage, we need to calculate the profit by comparing the cost price (CP) and selling price (SP) and then find the percentage increase from the cost price to the selling price.
Let's denote the cost price of one orange as 'c'. Since the cost price of 20 oranges is the same as the selling price of 12 oranges, we can set up the following equation: 20c = 12s, where 's' is the selling price per orange.
To find the selling price per orange, we can rearrange the equation to find 's': s = (20c/12). This indicates that each orange is sold at 5/3 times the cost price. Now, the gain per orange is s - c, which is (5/3c - c) or (2/3c) per orange.
The gain percentage is then calculated by the formula: (Gain/Cost Price) × 100%, which yields: ((2/3c)/c) × 100% = (2/3) × 100% = 66.(6)%.
Therefore, the gain in percentage is 66.67% (or 66 and 2/3 percent) when the selling price of 12 oranges equals the cost price of 20 oranges.