If selling price of an article is $\frac{4}{3}$ of its cost price, the profit in the transaction is (M.B.A., 2006)

### Concept & Profit from Ratios When the Selling Price (SP) is given as a fraction of the Cost Price (CP), it provides a direct ratio between SP and CP. We can use this ratio to find the profit fraction, and convert it directly to a percentage. $$ \text{Profit } \% = \frac{SP - CP}{CP} \times 100 $$ ### Step-by-Step Solution * Given: $SP = \frac{4}{3} \times CP$ * Rearrange to find the ratio: $\frac{SP}{CP} = \frac{4}{3}$ * Let SP be $4x$ and CP be $3x$. * Calculate Profit: $\text{Profit} = SP - CP = 4x - 3x = 1x$ * Calculate Profit Percentage: $\text{Profit } \% = (\frac{\text{Profit}}{CP}) \times 100$ * $\text{Profit } \% = (\frac{x}{3x}) \times 100 = \frac{1}{3} \times 100$ * $\frac{100}{3}\% = 33 \frac{1}{3}\%$ ### Exam Strategy & Shortcut Simply look at the fraction $\frac{4}{3}$. This means for every $3$ units of cost, the selling price is $4$ units. The profit is $1$ unit on a base of $3$ units. The fraction $\frac{1}{3}$ directly corresponds to the standard percentage $33 \frac{1}{3}\%$. ### Common Pitfall Calculating the profit percentage on the Selling Price instead of the Cost Price (i.e., using $1/4$ instead of $1/3$, which would incorrectly yield $25\%$). ### Final Answer Therefore, the correct answer is **$33 \frac{1}{3}\%$**.