A shopkeeper sells an article for ₹ 324 after giving a discount of 28% on its marked price. The cost price of the article is ₹300. If he sells the article by giving 18% discount on its same marked price, then what will be his profit percent ?

Question

Accepted Answer

To determine the profit percent when the shopkeeper sells the article with an 18% discount on its marked price, we need to follow these steps:

1. **Calculate the Marked Price (MP):**
   - The shopkeeper sells the article for ₹324 after giving a 28% discount.
   - Let the marked price be $ x $.
   - The selling price (SP) after a 28% discount is given by:
     $$
     SP = x - (0.28 \times x) = 0.72x
     $$
   - We know that $ SP = ₹324 $, so:
     $$
     0.72x = 324
     $$
   - Solving for $ x $:
     $$
     x = \frac{324}{0.72} = 450
     $$
   - Therefore, the marked price is ₹450.

2. **Calculate the Selling Price with an 18% Discount:**
   - With an 18% discount, the selling price is:
     $$
     SP = x - (0.18 \times x) = 0.82x
     $$
   - Substituting the marked price:
     $$
     SP = 0.82 \times 450 = 369
     $$

3. **Calculate the Profit Percent:**
   - The cost price (CP) of the article is ₹300.
   - Profit is given by:
     $$
     \text{Profit} = SP - CP = 369 - 300 = 69
     $$
   - Profit percent is calculated as:
     $$
     \text{Profit Percent} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{69}{300}\right) \times 100 = 23\%
     $$

Therefore, the profit percent when the shopkeeper sells the article with an 18% discount on its marked price is 23%, which corresponds to Option 3.

**Explanation of Incorrect Options:**

1. **Option 1 (0.1):** This option suggests a profit percent of 0.1%, which is incorrect because the calculated profit percent is significantly higher at 23%.

2. **Option 2 (0.19):** This option suggests a profit percent of 19%, which is also incorrect. The actual profit percent, as calculated, is 23%.

3. **Option 4 (0.24):** This option suggests a profit percent of 24%, which is slightly higher than the correct value. The precise calculation shows the profit percent to be 23%.

In conclusion, the correct profit percent when the shopkeeper sells the article with an 18% discount is 23%, making Option 3 the correct choice.