Final answer:
The question involves finding the selling price of an article at a 5% gain and 5% loss and then comparing the difference to the cost price. The equation formed from the question as presented (1.05C - 0.95C = C) suggests an error since the only solution to C would be 0, which is not feasible in real-world terms. Usually, questions of this nature are structured so that the difference equates to a known value instead of the cost price itself.
Step-by-step explanation:
The question is about calculating the selling price of an article at two different scenarios (profit and loss) and comparing the difference to its cost price. To find the selling prices with the data provided, we can create two equations based on the definition of profit and loss, where the profit is the amount earned above the cost price, and loss is the amount earned below the cost price.
Note that a 5% gain means the selling price is 105% of the cost price (C), or 1.05C. Similarly, a 5% loss means the selling price is 95% of the cost price, or 0.95C. According to the student's statement, the difference between the two selling prices (1.05C - 0.95C) is equal to the cost price (C).
To solve for C, you would set up an equation like this:
1.05C - 0.95C = C
0.10C = C
Since the only way for 0.10C to equal C is for C to be 0, which doesn't make sense in this scenario, there seems to be an issue with the question as stated. Typically, such a question might be phrased with the difference equating to a particular value, where C could be determined.