A person buys a shirt at 30% discount on the printed price and sells it at 12% profit on the printed price. Profit on cost price in percentage is :

Question

Accepted Answer

To determine the profit on the cost price in percentage, let's break down the problem step by step:

1. **Understanding the Purchase and Sale:**
   - The person buys a shirt at a 30% discount on the printed price.
   - The person sells the shirt at a 12% profit on the printed price.

2. **Calculating the Cost Price:**
   - Let the printed price of the shirt be $ P $.
   - The cost price (CP) after a 30% discount is $ P - 0.3P = 0.7P $.

3. **Calculating the Selling Price:**
   - The selling price (SP) is at a 12% profit on the printed price, which is $ P + 0.12P = 1.12P $.

4. **Calculating the Profit on Cost Price:**
   - Profit is calculated as the difference between the selling price and the cost price: $ \text{Profit} = SP - CP = 1.12P - 0.7P = 0.42P $.
   - The profit percentage on the cost price is given by:
     $$
     \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 = \left(\frac{0.42P}{0.7P}\right) \times 100 = 60\%
     $$

5. **Conclusion:**
   - The profit on the cost price is 60%, which corresponds to Option 3.

**Explanation of Incorrect Options:**

- **Option 1 (42%):** This option is incorrect because the calculation shows that the profit percentage on the cost price is 60%, not 42%.
  
- **Option 2 (48%):** This option is incorrect because the profit percentage calculated is 60%, not 48%.

- **Option 4 (64%):** This option is incorrect because the profit percentage on the cost price is 60%, not 64%.

Thus, the correct answer is Option 3, which is 60%.