The following questions are accompanied by two statements (A), (B). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
A shopkeeper sells articles at a certain profit. Find the amount of profit if the profit is 20%.
A. If the cost price increases by Rs 100 and selling price remains the same, the profit percentage becomes 12.5%
B. Marked price is Rs 500 above the cost price and average of SP and Marked price is Rs 1900.

Options

A. Statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the questions.
B. Statement B alone is sufficient to answer the question but statement A alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the questions.
D. Either statement A or statement B by itself is sufficient to answer the question.

Answer

To determine the amount of profit when the profit percentage is given as 20%, we analyze the provided statements (A) and (B) to see if either or both are sufficient to answer the question.

### Step-by-step Solution:

1. **Understanding the Problem:**
- We need to find the amount of profit when the profit percentage is 20%.
- Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100 \]

2. **Analyzing Statement A:**
- Statement A states: "If the cost price increases by Rs 100 and selling price remains the same, the profit percentage becomes 12.5%."
- Let the original cost price be \( CP = X \).
- The selling price at 20% profit is:
\[ SP = X + 0.2X = 1.2X \]
- If the cost price increases by Rs 100, the new cost price becomes \( CP' = X + 100 \).
- The new profit percentage is given as 12.5%, thus:
\[ \frac{SP - CP'}{CP'} \times 100 = 12.5 \]
- Substituting the values:
\[ \frac{1.2X - (X + 100)}{X + 100} \times 100 = 12.5 \]
- Simplifying this equation:
\[ \frac{1.2X - X - 100}{X + 100} \times 100 = 12.5 \]
\[ \frac{0.2X - 100}{X + 100} \times 100 = 12.5 \]
\[ 0.2X - 100 = 12.5 \times \frac{X + 100}{100} \]
\[ 0.2X - 100 = 0.125X + 12.5 \]
\[ 0.2X - 0.125X = 100 + 12.5 \]
\[ 0.075X = 112.5 \]
\[ X = \frac{112.5}{0.075} = 1500 \]
- Now, the original cost price \( CP = 1500 \).
- The profit amount can be calculated as:
\[ \text{Profit} = 0.2 \times 1500 = 300 \]

3. **Analyzing Statement B:**
- Statement B states: "Marked price is Rs 500 above the cost price and the average of SP and Marked price is Rs 1900."
- Let the cost price be \( CP = X \).
- Then the marked price \( MP = X + 500 \).
- The average of the selling price and marked price is given as:
\[ \frac{SP + MP}{2} = 1900 \]
- Substituting the value of \( MP \):
\[ \frac{SP + (X + 500)}{2} = 1900 \]
- Simplifying gives:
\[ SP + X + 500 = 3800 \]
\[ SP = 3800 - X - 500 = 3300 - X \]
- The profit percentage is given as 20%, thus:
\[ \frac{SP - CP}{CP} \times 100 = 20 \]
- Substituting the values:
\[ \frac{(3300 - X) - X}{X} \times 100 = 20 \]
\[ \frac{3300 - 2X}{X} \times 100 = 20 \]
\[ 3300 - 2X = 0.2X \]
\[ 3300 = 2.2X \]
\[ X = \frac{3300}{2.2} = 1500 \]
- The profit amount can again be calculated as:
\[ \text{Profit} = 0.2 \times 1500 = 300 \]

### Conclusion:
Both statements A and B are sufficient to determine the amount of profit, which is Rs 300.