To find the original cost of 6 pens and 2 pencils, let's set up a system of linear equations based on the information provided.

1. Define Variables

Let:

$x$ = Original cost of one pen

$y$ = Original cost of one pencil

2. Set Up the Equations

From the first statement:

The cost of 6 pens and 19 pencils is ₹275.

$$6x + 19y = 275 \quad \text{--- (Equation 1)}$$

From the second statement:

If the cost of a pen decreases by ₹7 ($x - 7$) and the cost of a pencil increases by ₹7 ($y + 7$), then the cost of 15 pens and 4 pencils is ₹132.

$$15(x - 7) + 4(y + 7) = 132$$

Simplify the equation:

$$15x - 105 + 4y + 28 = 132$$

$$15x + 4y - 77 = 132$$

$$15x + 4y = 209 \quad \text{--- (Equation 2)}$$

3. Solve the System of Equations

We have:

$6x + 19y = 275$

$15x + 4y = 209$

Multiply Equation 1 by 4 and Equation 2 by 19 to eliminate $y$:

$4(6x + 19y) = 4(275) \implies 24x + 76y = 1100$

$19(15x + 4y) = 19(209) \implies 285x + 76y = 3971$

Subtract the first from the second:

$$(285x - 24x) = 3971 - 1100$$

$$261x = 2871$$

$$x = \frac{2871}{261} = 11$$

Substitute $x = 11$ back into Equation 1:

$$6(11) + 19y = 275$$

$$66 + 19y = 275$$

$$19y = 209$$

$$y = \frac{209}{19} = 11$$

4. Calculate the Target Cost

The original cost of 6 pens and 2 pencils is:

$$\text{Cost} = 6x + 2y$$

$$\text{Cost} = 6(11) + 2(11)$$

$$\text{Cost} = 66 + 22 = 88$$

The original cost of 6 pens and 2 pencils is ₹88.