The marked price of an article is ₹ 840. A shopkeeper gives a discount of 15% on the marked price and still makes a profit of 19%. What is the cost price of the article ?

Question

Accepted Answer

To determine the cost price of the article, we need to consider the given information: the marked price, the discount offered, and the profit made by the shopkeeper.

1. **Marked Price and Discount:**
   - The marked price of the article is ₹ 840.
   - A discount of 15% is given on the marked price.
   - Therefore, the selling price after the discount is calculated as follows:
     $$
     \text{Discount} = 15\% \text{ of } 840 = \frac{15}{100} \times 840 = 126
     $$
     $$
     \text{Selling Price} = \text{Marked Price} - \text{Discount} = 840 - 126 = 714
     $$

2. **Profit Calculation:**
   - The shopkeeper makes a profit of 19% on the cost price.
   - Let the cost price be $ C $.
   - The selling price is related to the cost price by the profit percentage:
     $$
     \text{Selling Price} = C + 19\% \text{ of } C = C \times (1 + \frac{19}{100}) = C \times 1.19
     $$
   - We know the selling price is ₹ 714, so:
     $$
     714 = C \times 1.19
     $$
     $$
     C = \frac{714}{1.19} = 600
     $$

3. **Conclusion:**
   - The calculated cost price is ₹ 600, which matches Option 3.

4. **Explanation of Incorrect Options:**
   - **Option 1 (₹ 540):** If the cost price were ₹ 540, the selling price with a 19% profit would be $ 540 \times 1.19 = 642.6 $, which does not match the calculated selling price of ₹ 714.
   - **Option 2 (₹ 580):** If the cost price were ₹ 580, the selling price with a 19% profit would be $ 580 \times 1.19 = 690.2 $, which also does not match the calculated selling price of ₹ 714.
   - **Option 4 (₹ 640):** If the cost price were ₹ 640, the selling price with a 19% profit would be $ 640 \times 1.19 = 761.6 $, which exceeds the calculated selling price of ₹ 714.

Therefore, the correct cost price of the article is ₹ 600, which is Option 3.