The cost of 4 pens and 4 pencils boxes is Rs. 100. Three times the cost of a pen is Rs. 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen.

Options

A. 15
B. 10
C. 5
D. 20

Explanation

To solve the problem, we will first define the variables and then form the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( x \) = cost of one pen (in Rs)
- \( y \) = cost of one pencil box (in Rs)

### Step 2: Form the First Equation
According to the problem, the total cost of 4 pens and 4 pencil boxes is Rs. 100. This can be expressed as:
\[ 4x + 4y = 100 \]

To simplify, we can divide the entire equation by 4:
\[ x + y = 25 \] (Equation 1)

### Step 3: Form the Second Equation
The problem states that three times the cost of a pen is Rs. 15 more than the cost of a pencil box. This can be expressed as:
\[ 3x = y + 15 \]

Rearranging this gives us:
\[ 3x - y = 15 \] (Equation 2)

### Step 4: Solve the Equations
Now we have the following system of equations:
1. \( x + y = 25 \)
2. \( 3x - y = 15 \)

We can solve these equations using the substitution or elimination method. Here, we will use the elimination method.

Adding both equations:
\[ (x + y) + (3x - y) = 25 + 15 \]
This simplifies to:
\[ 4x = 40 \]
Now, divide both sides by 4:
\[ x = 10 \]

### Step 5: Find the Cost of a Pencil Box
Now that we have the value of \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 10 + y = 25 \]
Subtracting 10 from both sides gives:
\[ y = 15 \]

### Conclusion
The cost of a pen is Rs. 10 and the cost of a pencil box is Rs. 15.

### Summary of the Solution
- Cost of a pen (x) = Rs. 10
- Cost of a pencil box (y) = Rs. 15