The cost of 4 pens and 4 pencil boxes is Rs 100. Also, three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations and find both costs.
Pen = Rs 10 each; Pencil box = Rs 15 each.
Step 1: Assume variables.
Let the cost of one pen be \(p\) (in rupees).
Let the cost of one pencil box be \(b\) (in rupees).
Step 2: Form the first equation.
We are told that 4 pens and 4 pencil boxes cost Rs 100.
This means: \(4p + 4b = 100\).
Divide everything by 4 to make it simpler: \(p + b = 25\).
Step 3: Form the second equation.
We are told that three times the cost of a pen is Rs 15 more than the cost of a pencil box.
So: \(3p = b + 15\).
Or we can write it as: \(b = 3p - 15\).
Step 4: Solve the equations.
From the first equation: \(p + b = 25\).
Now replace \(b\) with \(3p - 15\) (from the second equation):
\(p + (3p - 15) = 25\).
That gives: \(4p - 15 = 25\).
Add 15 on both sides: \(4p = 40\).
Divide by 4: \(p = 10\).
Step 5: Find the cost of the pencil box.
Use \(b = 3p - 15\).
Put \(p = 10\): \(b = 3(10) - 15 = 30 - 15 = 15\).
Final Answer: Pen costs Rs 10 each, and Pencil box costs Rs 15 each.