An article is sold at a certain price. By selling it at 5/7th of that price on loss 20%. Find the gain percentage at the original sold price.

Given:
Let the original selling price be 'x'
New selling price = (5/7)x
Loss on new selling price = 20%

​If selling at (5/7)x results in a 20% loss, it means:​​

​$$\frac{5}{7}x = 0.8 \times \text{Cost Price}$$​​

​$$\text{Cost Price} = \frac{25}{28}x$$

Gain = Original Selling Price - Cost Price

$$\text{Gain} = x - \frac{25}{28}x = \frac{3}{28}x$$​​​

​$$\text{Gain percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100$$​​

​$$\text{Gain Percentage} = \left( \frac{\frac{3}{28}x}{\frac{25}{28}x} \right) \times 100$$​​

​$$\text{Gain Percentage} = \left( \frac{3}{25} \right) \times 100 = 12\%$$​​

Hence, the gain percentage at the original selling price is 12%.