If the cost price of 24 articles is equal to the selling price of 15 articles, then find the percentage of profit.

The correct option is 60%.

Let the cost price (CP) of one article be $\mathrm{CP}$ and the selling price (SP) of one article be $\mathrm{SP}$.

According to the question, the cost price of 24 articles is equal to the selling price of 15 articles. Therefore, we can write:
$24\times \mathrm{CP}=15\times \mathrm{SP}$

From this relation, we can find the ratio of the selling price to the cost price:
$\frac{\mathrm{SP}}{\mathrm{CP}}=\frac{24}{15}$

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3, we get:
$\frac{\mathrm{SP}}{\mathrm{CP}}=\frac{8}{5}$

This ratio indicates that if the cost price (CP) is 5 units, the selling price (SP) is 8 units.

The profit earned is calculated as:
$\text{Profit}=\mathrm{SP}-\mathrm{CP}$
$\text{Profit}=8-5=3\text{units}$

Now, we can find the profit percentage using the formula:
$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\mathrm{CP}}\right)\times 100$

Substituting the values into the formula:
$\text{Profit Percentage}=\left(\frac{3}{5}\right)\times 100$

Simplifying further:
$\text{Profit Percentage}=3\times 20=60\%$

Thus, the profit percentage is 60%.