If the cost price of 24 articles is equal to the selling price of 18 articles, then the percentage profit is :

Question

Accepted Answer

To determine the percentage profit, we need to understand the relationship between the cost price (CP) and the selling price (SP) given in the problem. The problem states that the cost price of 24 articles is equal to the selling price of 18 articles.

Let's denote:
- CP of 1 article as $ C $
- SP of 1 article as $ S $

According to the problem:
$$ 24C = 18S $$

From this equation, we can express the selling price in terms of the cost price:
$$ S = \frac{24C}{18} = \frac{4C}{3} $$

The profit per article is the difference between the selling price and the cost price:
$$ \text{Profit per article} = S - C = \frac{4C}{3} - C = \frac{4C}{3} - \frac{3C}{3} = \frac{C}{3} $$

The percentage profit is calculated as:
$$ \text{Percentage Profit} = \left(\frac{\text{Profit per article}}{\text{Cost price per article}}\right) \times 100\% = \left(\frac{\frac{C}{3}}{C}\right) \times 100\% = \frac{1}{3} \times 100\% = 33\frac{1}{3}\% $$

Therefore, the percentage profit is $ 33\frac{1}{3}\% $, which corresponds to Option 4.

**Explanation of why other options are incorrect:**

1. **Option 1: 25$\frac{1}{3}$%** - This option suggests a lower percentage profit than calculated. The calculation clearly shows that the profit is $ \frac{C}{3} $ per article, leading to a percentage profit of $ 33\frac{1}{3}\% $, not $ 25\frac{1}{3}\% $.

2. **Option 2: 31$\frac{1}{3}$%** - This option is also incorrect as it underestimates the percentage profit. The correct calculation based on the given relationship between CP and SP results in $ 33\frac{1}{3}\% $.

3. **Option 3: 16$\frac{2}{3}$%** - This option significantly underestimates the profit percentage. The derived formula and calculation show that the profit is much higher, specifically $ 33\frac{1}{3}\% $.

In conclusion, the correct percentage profit is $ 33\frac{1}{3}\% $, which is why Option 4 is the correct answer.