20 pens and 46 pencils were purchased for Rs. 235. If the average price of a pencil is Rs 2.50 then calculate the average price (in RS.) of a pen.
A. 6
B. 4
C. 8
D. 12

Options

A. B
B. C
C. A
D. D

Answer

To solve the problem step by step, we need to find the average price of a pen given the total cost of pens and pencils, as well as the average price of a pencil.

### Step 1: Identify the variables
Let:
- \( x \) = average price of a pen (in Rs.)
- \( y \) = average price of a pencil (in Rs.)

From the problem, we know:
- \( y = 2.50 \) (the average price of a pencil)
- Total number of pens = 20
- Total number of pencils = 46
- Total cost = Rs. 235

### Step 2: Write the equation for total cost
The total cost can be expressed as:
\[ \text{Total Cost} = (\text{Number of Pens} \times \text{Price of Pen}) + (\text{Number of Pencils} \times \text{Price of Pencil}) \]
Substituting the known values:
\[ 235 = (20 \times x) + (46 \times 2.50) \]

### Step 3: Calculate the total cost of pencils
Calculate the total cost of the pencils:
\[ 46 \times 2.50 = 115 \]

### Step 4: Substitute the cost of pencils into the equation
Now substitute this value back into the equation:
\[ 235 = 20x + 115 \]

### Step 5: Solve for the price of a pen
Rearranging the equation to isolate \( x \):
\[ 20x = 235 - 115 \]
\[ 20x = 120 \]
Now divide both sides by 20:
\[ x = \frac{120}{20} = 6 \]

### Conclusion
The average price of a pen is Rs. 6.

### Final Answer
The average price of a pen is **Rs. 6** (Option A).

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