Unitary Method

To solve this problem, we'll use ratio and proportion concepts. First, we know the total cost of 6 pens and 9 pencils is ₹126. We can set up the following equations:

Let the cost of a pen be ₹p and the cost of a pencil be ₹q.

So, 6p + 9q = 126 (Equation 1).

We want to determine the cost of 8 pens and 12 pencils:

Observe that 8 pens and 12 pencils is basically (4/3) times 6 pens and 9 pencils:

Ratio of (8 pens + 12 pencils) to (6 pens + 9 pencils) is 4/3;

To find the cost:

Substitute the known value from Equation 1:

This simplifies to:

Therefore, the total cost of 8 pens and 12 pencils is ₹168.

The decimal number can be converted to a fraction by following these steps:

1. Let . This means

2. Multiply both sides by to shift the decimal point past the repeating part:

3. Again, multiply by to shift the decimal to align with the repeating sequence:

4. Subtract the equation from step 3 from the equation in step 2:

5. Simplify the equations:

6. Now, solve for by dividing both sides by :