If 70% of the cost price of an article is equal to 40% of its selling price, what is the profit percentage?

The correct answer is 75%.

Step-by-step solution:

1. Let the cost price of the article be denoted as $\mathrm{CP}$ and the selling price be denoted as $\mathrm{SP}$.

2. According to the question, 70% of the cost price is equal to 40% of the selling price:

$70\%\times \mathrm{CP}=40\%\times \mathrm{SP}$

3. Expressing the percentages as fractions or decimals:

$\frac{70}{100}\times \mathrm{CP}=\frac{40}{100}\times \mathrm{SP}$

4. Simplifying the equation by canceling out 100 from both denominators:

$70\times \mathrm{CP}=40\times \mathrm{SP}$

5. Finding the ratio of selling price ($\mathrm{SP}$) to cost price ($\mathrm{CP}$):

$\frac{\mathrm{SP}}{\mathrm{CP}}=\frac{70}{40}=\frac{7}{4}$

6. Now, calculate the profit:

$\text{Profit}=\mathrm{SP}-\mathrm{CP}$

7. The profit percentage is given by the formula:

$\text{Profit Percentage}=\left(\frac{\mathrm{SP}-\mathrm{CP}}{\mathrm{CP}}\right)\times 100$

$\text{Profit Percentage}=\left(\frac{\mathrm{SP}}{\mathrm{CP}}-1\right)\times 100$

8. Substitute the ratio $\frac{\mathrm{SP}}{\mathrm{CP}}=\frac{7}{4}$ into the profit percentage formula:

$\text{Profit Percentage}=\left(\frac{7}{4}-1\right)\times 100$

$\text{Profit Percentage}=\left(\frac{3}{4}\right)\times 100=75\%$

Thus, the profit percentage is 75%.