The following questions are accopanied by three statements (A) or (I), (B) or (II), and (C) or (III). You have to determine which statement(s) is/are sufficient/necessary to answer the questions.
What is the cost price of an article?
A.-After allowing a discount of 15% on marked price the shopkeeper charges Rs 1020 for it.
B. If he had not allowed any discount, he would have had a profit of `47 (1)/(17)%.`
C. If he had allowed only 10% discount on marked price, he would have had `32 (6)/(17)%` profit

Options

A. Any two of them
B. Only A and B together
C. Only B and C together
D. A and either B or C

Answer

To determine the cost price of an article, we will analyze the statements provided one by one and see if they are sufficient to answer the question.

### Step-by-Step Solution:

1. **Understanding Statement A**:
- Statement A states that after allowing a discount of 15% on the marked price, the shopkeeper charges Rs 1020.
- Let the marked price be \( MP \).
- The selling price after the discount is given by:
\[ SP = MP \times \left(1 - \frac{15}{100}\right) = MP \times \frac{85}{100} \]
- Setting this equal to Rs 1020:
\[ MP \times \frac{85}{100} = 1020 \]
- Rearranging gives:
\[ MP = \frac{1020 \times 100}{85} = 1200 \]
- However, we need to find the cost price (CP), and we cannot determine CP from this statement alone. Thus, **Statement A is not sufficient**.

2. **Understanding Statement B**:
- Statement B states that if no discount was allowed, the profit would have been \( 47 \frac{1}{17}\% \).
- This can be converted to an improper fraction:
\[ 47 \frac{1}{17} = \frac{800}{17}\% \]
- If the marked price is Rs 1200 (from Statement A), then the selling price without discount is also Rs 1200.
- The profit percentage formula is:
\[ \text{Profit} = \frac{SP - CP}{CP} \times 100 \]
- Rearranging gives:
\[ SP = CP \times \left(1 + \frac{Profit}{100}\right) \]
- Substituting the values:
\[ 1200 = CP \times \left(1 + \frac{800/17}{100}\right) \]
- This equation can be solved for CP, thus **Statement B is sufficient**.

3. **Understanding Statement C**:
- Statement C states that if a 10% discount was given on the marked price, the profit would have been \( 32 \frac{6}{17}\% \).
- Converting to an improper fraction:
\[ 32 \frac{6}{17} = \frac{550}{17}\% \]
- The selling price with a 10% discount on the marked price of Rs 1200 is:
\[ SP = 1200 \times \left(1 - \frac{10}{100}\right) = 1200 \times 0.9 = 1080 \]
- Using the profit percentage formula:
\[ 1080 = CP \times \left(1 + \frac{550/17}{100}\right) \]
- This equation can also be solved for CP, thus **Statement C is sufficient**.

### Conclusion:
- **Statement A** alone is not sufficient.
- **Statement B** alone is sufficient.
- **Statement C** alone is sufficient.

Since we can find the cost price using either Statement B or Statement C along with Statement A, the answer is that we need **Statement A and either Statement B or Statement C**.

### Final Answer:
The correct option is **A and either B or C**.