An article is sold at a certain price by selling the article at 2/3 (two third) of that price, there is a loss of 10%. Find the gain percent at its original price.

The correct option is 35%.

To find the gain percentage at the original selling price, we can break down the relationship between the cost price, the original selling price, and the new selling price step-by-step.

Step 1: Define the variables
Let the original selling price of the article be $S$.
Let the cost price of the article be $C$.

Step 2: Relate the new selling price to the cost price
According to the problem, if the article is sold at $\frac{2}{3}$ of its original price, there is a loss of 10%.
A loss of 10% means the new selling price is equal to 90% of the cost price $C$.

Therefore, we can write the equation: $$\frac{2}{3}S=90\%\text{of}C$$

Expressing 90% as a fraction: $$\frac{2}{3}S=\frac{90}{100}C$$

Simplifying the fraction: $$\frac{2}{3}S=\frac{9}{10}C$$

Step 3: Solve for the original selling price $S$ in terms of $C$
Multiply both sides of the equation by $\frac{3}{2}$: $$S=\frac{9}{10}\times \frac{3}{2}C$$

$$S=\frac{27}{20}C$$

Converting the fraction to a decimal: $$S=1.35C$$

Step 4: Find the gain percent at the original price
The original selling price is 1.35 times the cost price, which indicates a gain. The gain is calculated as: $$\text{Gain}=S-C$$

$$\text{Gain}=1.35C-C=0.35C$$

Now, calculate the gain percentage: $$\text{Gain Percent}=\left(\frac{\text{Gain}}{C}\right)\times 100\%$$

$$\text{Gain Percent}=\left(\frac{0.35C}{C}\right)\times 100\%=35\%$$

Thus, the gain percentage when the article is sold at its original price is 35%.