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 and a pencil box.

Options

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

Explanation

To solve the problem, we will follow these steps:

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

### Step 2: Formulate the First Equation
According to the first condition, the cost of 4 pens and 4 pencil boxes is Rs. 100. This can be expressed as:
\[ 4x + 4y = 100 \]
We can simplify this equation by dividing all terms by 4:
\[ x + y = 25 \]
This is our first equation.

### Step 3: Formulate the Second Equation
According to the second condition, 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:
\[ 3x - y = 15 \]
This is our second equation.

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

### Step 5: Solve the Equations
To solve these equations, we can use the elimination method. We will add both equations to eliminate \( y \).

Adding Equation 1 and Equation 2:
\[ (x + y) + (3x - y) = 25 + 15 \]
This simplifies to:
\[ 4x = 40 \]
Now, divide both sides by 4:
\[ x = 10 \]

### Step 6: Substitute to Find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 10 + y = 25 \]
Subtracting 10 from both sides gives:
\[ y = 15 \]

### Step 7: Conclusion
The cost of one pen is Rs. 10 and the cost of one pencil box is Rs. 15.

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

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