A shopkeeper sold an article for ₹540 at some profit. Had he sold it for ₹470, then there would have been a loss equal to one-sixth of the initial profit. What was the cost price (in ₹) of the article?

Options

A. 525
B. 480
C. 505
D. 540

Answer

To find the cost price of the article, let's denote the cost price as \( CP \).

1. **Understanding the Selling Prices and Profit**:
- The shopkeeper sold the article for ₹540 at some profit.
- Therefore, the profit can be expressed as:
\[ Profit = Selling Price - Cost Price = 540 - CP \]

2. **Understanding the Loss Scenario**:
- If the shopkeeper sold the article for ₹470, there would be a loss.
- The loss in this case can be expressed as:
\[ Loss = Cost Price - Selling Price = CP - 470 \]
- According to the problem, this loss is equal to one-sixth of the initial profit:
\[ CP - 470 = \frac{1}{6}(540 - CP) \]

3. **Setting Up the Equation**:
- We can now set up the equation based on the information we have:
\[ CP - 470 = \frac{1}{6}(540 - CP) \]

4. **Eliminating the Fraction**:
- To eliminate the fraction, multiply both sides by 6:
\[ 6(CP - 470) = 540 - CP \]
- This simplifies to:
\[ 6CP - 2820 = 540 - CP \]

5. **Rearranging the Equation**:
- Now, let's rearrange the equation to isolate \( CP \):
\[ 6CP + CP = 540 + 2820 \]
\[ 7CP = 3360 \]

6. **Solving for Cost Price**:
- Finally, divide both sides by 7 to find \( CP \):
\[ CP = \frac{3360}{7} = 480 \]

Thus, the cost price of the article is **₹480**.