What is the labelled price of the article?
I. Cost price of the article is Rs.500/.
II. Selling price after offering `5%` discount on the labelled price is Rs. 608/.
III. Profit earned would have been `28%` in no discount was offered.

Options

A. Only I
B. Only II
C. Only II & III
D. Only I and II

Explanation

To determine the labeled price of the article, we can analyze the given statements step by step.

### Step 1: Analyze Statement I
Statement I states that the cost price (CP) of the article is Rs. 500.
- While this gives us information about the cost price, it does not directly help us find the labeled price (LP).

**Conclusion**: Statement I alone is not sufficient.

### Step 2: Analyze Statement II
Statement II states that the selling price (SP) after offering a 5% discount on the labeled price is Rs. 608.
- Let the labeled price be denoted as \( X \).
- The selling price after a 5% discount can be expressed as:
\[ SP = LP - (5\% \text{ of } LP) = X - \frac{5}{100}X = 0.95X \]
- According to Statement II, we have:
\[ 0.95X = 608 \]
- To find \( X \), we can rearrange the equation:
\[ X = \frac{608}{0.95} \]
- Calculating this gives:
\[ X = \frac{608 \times 100}{95} = \frac{60800}{95} \approx 640 \]

**Conclusion**: Statement II alone is sufficient to find the labeled price.

### Step 3: Analyze Statement III
Statement III states that the profit earned would have been 28% if no discount was offered.
- The selling price without any discount can be expressed as:
\[ SP = CP + \text{Profit} = CP + 28\% \text{ of } CP \]
- Given that the cost price (CP) is Rs. 500, we can calculate the selling price:
\[ SP = 500 + 0.28 \times 500 = 500 + 140 = 640 \]
- This means that if no discount was offered, the selling price would be Rs. 640, which is also equal to the labeled price since the selling price without discount is the labeled price.

**Conclusion**: Statement III alone is also sufficient to find the labeled price.

### Final Conclusion
- Statement II alone is sufficient to determine the labeled price.
- Statement III alone is also sufficient to determine the labeled price.
- Therefore, we can conclude that the answer to the question is that either Statement II or Statement III is sufficient.

### Answer:
The labeled price of the article is Rs. 640.

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