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 ?

Question

Accepted Answer

To determine the profit percent when the article is sold at its marked price, we need to follow these steps:

1. **Determine the Marked Price (MP):**
   - The article is sold for ` 608 after a 24% discount on the marked price.
   - Let the marked price be ` x.
   - Given that a 24% discount on the marked price results in a selling price of ` 608, we can write:
     $$
     x - 0.24x = 608
     $$
     $$
     0.76x = 608
     $$
     $$
     x = \frac{608}{0.76} = 800
     $$
   - Therefore, the marked price is ` 800.

2. **Calculate the Profit if Sold at Marked Price:**
   - If the article is sold at its marked price of ` 800, the selling price (SP) would be ` 800.
   - The cost price (CP) of the article is given as ` 750.
   - Profit = Selling Price - Cost Price = ` 800 - ` 750 = ` 50.

3. **Calculate the Profit Percent:**
   - Profit percent is calculated as:
     $$
     \text{Profit Percent} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100
     $$
     $$
     \text{Profit Percent} = \left(\frac{50}{750}\right) \times 100 = \frac{1}{15} \times 100 = 6.\overline{6}\%
     $$
   - This is equivalent to 6$\frac{2}{3}$%.

4. **Explanation of Options:**
   - **Option 1: 6$\frac{2}{3}$%** is correct as calculated above.
   - **Option 2: 0.05** is incorrect because 0.05 as a percentage is 5%, which does not match the calculated profit percent.
   - **Option 3: 0.06** is incorrect because 0.06 as a percentage is 6%, which is not the calculated profit percent.
   - **Option 4: 5$\frac{1}{3}$%** is incorrect because it represents approximately 5.33%, which is not the calculated profit percent.

Therefore, the correct answer is Option 1: 6$\frac{2}{3}$%.