Each question consists of a question and two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate option.
A shopkeeper sold two articles, A and B, at a profit of `30%` and `40%`respectively. What is the overall profit earned by the shopkeeper after selling both articles (A and B)?
I Had shopkeeper sold article A at a profit of `20%` and article B at a loss of `10%`, the selling price of both the articles would have been the same.
II. The cost price of article B is 200 more than the cost price of article A.

Options

A. The data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question.
B. The data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.
C. The data either in statement I alone or in statement II alone are sufficient to answer the question.
D. The data in both the statements I and II together are necessary to answer the question.

Answer

To solve the problem, we need to determine the overall profit earned by the shopkeeper after selling two articles, A and B, at different profit percentages. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Profit Percentages**:
- Article A is sold at a profit of 30%.
- Article B is sold at a profit of 40%.

2. **Let’s Define Variables**:
- Let the cost price of article A be \( CP_A \).
- Let the cost price of article B be \( CP_B \).

3. **Calculating Selling Prices**:
- The selling price of article A (SP_A) can be calculated as:
\[ SP_A = CP_A + 0.3 \times CP_A = 1.3 \times CP_A \]
- The selling price of article B (SP_B) can be calculated as:
\[ SP_B = CP_B + 0.4 \times CP_B = 1.4 \times CP_B \]

4. **Overall Profit Calculation**:
- The overall profit can be determined by calculating the total selling price minus the total cost price:
\[ \text{Overall Profit} = (SP_A + SP_B) - (CP_A + CP_B) \]
- Substituting the expressions for SP_A and SP_B:
\[ \text{Overall Profit} = (1.3 \times CP_A + 1.4 \times CP_B) - (CP_A + CP_B) \]
- Simplifying this gives:
\[ \text{Overall Profit} = (1.3 \times CP_A - CP_A) + (1.4 \times CP_B - CP_B) = 0.3 \times CP_A + 0.4 \times CP_B \]

5. **Using the Statements**:
- **Statement I**: If the shopkeeper sold article A at a profit of 20% and article B at a loss of 10%, the selling price of both articles would have been the same.
- This gives us the equation:
\[ 1.2 \times CP_A = 0.9 \times CP_B \]
- **Statement II**: The cost price of article B is 200 more than the cost price of article A.
- This gives us the equation:
\[ CP_B = CP_A + 200 \]

6. **Combining the Statements**:
- From Statement I, we can express \( CP_B \) in terms of \( CP_A \):
\[ CP_B = \frac{1.2}{0.9} \times CP_A = \frac{4}{3} \times CP_A \]
- From Statement II, we have:
\[ CP_B = CP_A + 200 \]
- Setting these two expressions for \( CP_B \) equal to each other:
\[ \frac{4}{3} \times CP_A = CP_A + 200 \]
- Solving this equation will allow us to find the cost prices of A and B.

7. **Final Calculation**:
- Solving the equation:
\[ \frac{4}{3} CP_A - CP_A = 200 \]
\[ \frac{1}{3} CP_A = 200 \implies CP_A = 600 \]
- Substituting back to find \( CP_B \):
\[ CP_B = CP_A + 200 = 600 + 200 = 800 \]
- Now we can calculate the overall profit:
\[ \text{Overall Profit} = 0.3 \times 600 + 0.4 \times 800 = 180 + 320 = 500 \]

### Conclusion:
The overall profit earned by the shopkeeper after selling both articles A and B is **500**.