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.
Calculate the marked price of item?
(I) Shopkeeper marked the article 80% above its cost price and shopkeeper earned Rs.100 profit on the article.
(II) Ratio of marked price and discount allowed on the article is 3:1.

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) alore 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 solve the problem of calculating the marked price of an item based on the provided statements, we will analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** The shopkeeper marked the article 80% above its cost price and earned Rs. 100 profit on the article.

Let the cost price (CP) be denoted as \( x \).

The marked price (MP) can be calculated as:
\[ MP = CP + 80\% \text{ of CP} = x + 0.8x = 1.8x \]

The selling price (SP) is given by:
\[ SP = CP + Profit = x + 100 \]

### Step 2: Set Up the Equation
From the relationship between marked price, selling price, and cost price, we know that:
\[ SP = MP - Discount \]
However, we do not have information about the discount from Statement I alone. Therefore, we cannot determine the marked price solely from this statement.

### Conclusion for Statement I
**Statement I alone is not sufficient to answer the question.**

### Step 3: Analyze Statement II
**Statement II:** The ratio of marked price and discount allowed on the article is 3:1.

Let the discount be denoted as \( y \). According to the statement:
\[ \frac{MP}{y} = \frac{3}{1} \implies MP = 3y \]

### Step 4: Relate Both Statements
We have two expressions for the marked price:
1. From Statement I: \( MP = 1.8x \)
2. From Statement II: \( MP = 3y \)

Setting these equal gives us:
\[ 1.8x = 3y \implies y = \frac{1.8x}{3} = 0.6x \]

### Step 5: Calculate Selling Price Using Both Statements
Using the relationship between selling price, marked price, and discount:
\[ SP = MP - y \]
Substituting the values we have:
\[ SP = 3y - y = 2y \]
Substituting for \( y \):
\[ SP = 2(0.6x) = 1.2x \]

### Step 6: Set Up the Final Equation
From Statement I, we also know:
\[ SP = x + 100 \]
Setting these equal:
\[ 1.2x = x + 100 \]

### Step 7: Solve for x
Rearranging gives:
\[ 1.2x - x = 100 \implies 0.2x = 100 \implies x = \frac{100}{0.2} = 500 \]

### Step 8: Calculate Marked Price
Now substituting \( x \) back into the equation for marked price:
\[ MP = 1.8x = 1.8 \times 500 = 900 \]

### Final Answer
The marked price of the item is Rs. 900.

### Conclusion for Both Statements
Both statements together are necessary to answer the question, but neither statement alone is sufficient.