The cost price of an article is ₹750. It is sold for ₹608 by giving 24% discount on its marked price. Had it been sold on its marked price, then what would have been the profit percent ?

The correct option is $6\frac{2}{3}\%$.

Step-by-step Explanation:

1. Identify the given values:
Cost Price (CP) of the article = ₹750
Selling Price (SP) of the article = ₹608
Discount percentage = 24%

2. Find the Marked Price (MP):
The Selling Price is obtained after giving a 24% discount on the Marked Price.
This means:
$\text{Selling Price}=\text{Marked Price}\times (100-24)\%$
$608=\text{Marked Price}\times \frac{76}{100}$

Solving for Marked Price (MP):
$\text{Marked Price}=\frac{608\times 100}{76}$
$\text{Marked Price}=8\times 100=\text{₹800}$

3. Calculate profit if sold at Marked Price:
If the article is sold at its Marked Price, then:
New Selling Price = Marked Price = ₹800
Profit = New Selling Price - Cost Price
$\text{Profit}=800-750=\text{₹50}$

4. Calculate the Profit Percentage:
$\text{Profit Percent}=\left(\frac{\text{Profit}}{\text{Cost Price}}\right)\times 100$
$\text{Profit Percent}=\left(\frac{50}{750}\right)\times 100$
$\text{Profit Percent}=\frac{1}{15}\times 100=\frac{20}{3}\%=6\frac{2}{3}\%$

Thus, if the article had been sold at its marked price, the profit percent would have been $6\frac{2}{3}\%$.