The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
Find profit percentage earned by shopkeeper on selling the article.
I. Ratio of cost price of an article to mark price of an article is 4 : 7 and ratio of discount allowed on article to profit earned on article is 49:11.
II. Discount allowed on article is Rs.190 more than profit earned on the article.

Options

A. Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question
B. Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.
D. Either statement (I) or statement (II) by itself is sufficient to answer the question.

Answer

To determine the profit percentage earned by a shopkeeper on selling an article, we will analyze the two statements provided and see if they are sufficient to answer the question.

### Step 1: Analyze Statement I
Statement I provides two ratios:
1. The ratio of the cost price (CP) to the mark price (MP) is 4:7.
2. The ratio of the discount allowed (D) to the profit earned (P) is 49:11.

From the first ratio, we can express CP and MP in terms of a variable \( k \):
- Let CP = \( 4k \)
- Let MP = \( 7k \)

From the second ratio, we can express D and P in terms of another variable \( m \):
- Let D = \( 49m \)
- Let P = \( 11m \)

### Step 2: Relate CP, MP, D, and P
The selling price (SP) can be calculated using the formula:
\[ SP = MP - D \]

Substituting the values we have:
\[ SP = 7k - 49m \]

The profit (P) is also defined as:
\[ P = SP - CP \]
Substituting the values:
\[ 11m = (7k - 49m) - 4k \]
This simplifies to:
\[ 11m = 3k - 49m \]
Rearranging gives:
\[ 11m + 49m = 3k \]
\[ 60m = 3k \]
Thus, we find:
\[ k = 20m \]

### Step 3: Calculate CP and P
Now substituting back to find CP and P:
- CP = \( 4k = 4(20m) = 80m \)
- P = \( 11m \)

### Step 4: Calculate Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{P}{CP} \right) \times 100 \]

Substituting the values we found:
\[ \text{Profit Percentage} = \left( \frac{11m}{80m} \right) \times 100 \]
The \( m \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{11}{80} \right) \times 100 = \frac{1100}{80} = 13.75\% \]

### Conclusion for Statement I
Statement I alone is sufficient to determine the profit percentage.

### Step 5: Analyze Statement II
Statement II states:
- The discount allowed on the article is Rs. 190 more than the profit earned on the article.

This gives us the equation:
\[ D = P + 190 \]

However, without knowing either D or P, we cannot determine the profit percentage. Therefore, Statement II alone is not sufficient.

### Final Conclusion
- **Statement I alone is sufficient.**
- **Statement II alone is not sufficient.**

Thus, the answer is that **Statement I alone is sufficient to answer the question.**