A person can purchage three articles in Rs49. What is the price of costliest article?
Statements:
The cost price of two articles each is Rs 1 less than the cost price of costliest article.
The cost price of two article is same.
The cost price of costliest article is `6.25%` more than the cost price of cheapest article.

Options

A. Data in either statement I alone or statements II and III together are sufficient to answer the question.
B. Data is only statement III is sufficient to answer the question
C. Data is only statement I and II together are sufficient to answer the question
D. Data is only statement I and III together are sufficient to answer the question

Answer

To solve the problem, we need to determine the price of the costliest article based on the given statements. Let's break down the solution step by step.

### Step 1: Define Variables
Let the cost price of the costliest article be denoted as \( x \). According to the statements:
- The cost price of the two other articles is \( x - 1 \) each.

### Step 2: Set Up the Equation
Since the total cost of the three articles is Rs 49, we can set up the following equation:
\[ x + (x - 1) + (x - 1) = 49 \]

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ x + (x - 1) + (x - 1) = 49 \]
\[ x + x - 1 + x - 1 = 49 \]
\[ 3x - 2 = 49 \]

### Step 4: Solve for \( x \)
Now, add 2 to both sides:
\[ 3x = 49 + 2 \]
\[ 3x = 51 \]
Now, divide both sides by 3:
\[ x = \frac{51}{3} = 17 \]

### Step 5: Conclusion
Thus, the price of the costliest article is Rs 17.