By selling an article at some price, a man gains $10\%$. If the article is sold at twice of the price, the gain percent will be (R.R.B., 2006)

### Concept & Multiplier Effect on Profit When an article's selling price (SP) changes relative to a fixed cost price (CP), the profit margins change dramatically. We can assume a base cost price of $100$ to make percentage calculations trivial, as a gain of $r\%$ on a CP of $100$ is exactly an SP of $100 + r$. $$ \text{New Gain } \% = \frac{\text{New SP} - \text{CP}}{\text{CP}} \times 100 $$ ### Step-by-Step Solution * Let the Cost Price (CP) of the article be $100$. * Given: The initial gain is $10\%$. * Initial Selling Price (SP1) = $\text{CP} + 10\% \text{ of CP} = 100 + 10 = 110$. * Given: The new Selling Price is twice the initial price. * New Selling Price (SP2) = $2 \times \text{SP1} = 2 \times 110 = 220$. * The Cost Price remains constant at $100$. * Calculate New Gain: $\text{New Gain} = \text{SP2} - \text{CP} = 220 - 100 = 120$. * Calculate New Gain Percentage: $(\frac{\text{New Gain}}{\text{CP}}) \times 100 = (\frac{120}{100}) \times 100 = 120\%$. ### Exam Strategy & Shortcut Simply visualize the multipliers. $\text{SP}_1 = 1.1 \text{CP}$. $\text{SP}_2 = 2 \times \text{SP}_1 = 2 \times (1.1 \text{CP}) = 2.2 \text{CP}$. Since the new SP is $2.2$ times the CP, it represents a $120\%$ increase over the original $1.0 \text{CP}$. Thus, the new gain is $120\%$. ### Common Pitfall A common reflex is to simply double the profit percentage since the price doubled (i.e., $10\% \times 2 = 20\%$). However, doubling the selling price adds the entire value of the original selling price to the profit margin, not just the original profit portion. ### Final Answer Therefore, the correct answer is **$120\%$**.