If the cost price of 24 pens is equal to the selling price of 18 pens, find the profit per cent.

Correct option is D

Given:

Let the cost price of each pen be CP and the selling price of each pen be SP .

It is given that the cost price of 24 pens is equal to the selling price of 18 pens.

Therefore, $$24 \times CP = 18 \times SP$$​​

Concept Used:
Simplifying the equation to find the ratio of SP to CP :

​$$\frac{SP}{CP} = \frac{24}{18} = \frac{4}{3}$$​​

Solution:
Thus, the selling price is  $$\frac{4}{3}$$ times the cost price, indicating a profit.

The profit percent is given by:

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

Substitute  $$SP = \frac{4}{3} CP$$​ into the formula:

​$$\text{Profit \%} = \left( \frac{\frac{4}{3} CP - CP}{CP} \right) \times 100$$​​

​$$\text{Profit \%} = \left( \frac{1}{3} \right) \times 100 = 33.33 \%$$​​

Therefore, the profit percent is 33.33%.