Let the cost price (CP) of a single article be denoted by \(x\). Consequently, the total CP for 90 articles is \(90x\). The problem states that the selling price (SP) of 75 articles is equivalent to the CP of 90 articles, meaning \(SP_{75} = 90x\). Therefore, the SP of one article is calculated as \(\frac{90x}{75}\), which simplifies to \(\frac{6x}{5}\). The gain on each article is the difference between its SP and CP: \(\frac{6x}{5} - x = \frac{6x - 5x}{5} = \frac{x}{5}\). The gain percentage is determined by the formula \(\frac{\text{Gain}}{\text{CP}} \times 100\), which in this case is \(\frac{\frac{x}{5}}{x} \times 100 = \frac{1}{5} \times 100 = 20\%\).