Define Variables for Original Costs

Let the original cost of a pen be represented by $p$ and the original cost of a pencil be represented by $c$. All costs are in Rupees (₹).

Formulate Algebraic Equations

Based on the problem statement, we can set up two linear equations:

• Equation 1: The cost of 7 pens and 8 pencils is ₹230.

  $7p + 8c = 230$

• Equation 2: If the cost of a pen decreases by ₹1 (new cost $p-1$) and the cost of a pencil increases by ₹7 (new cost $c+7$), the cost of 14 pens and 4 pencils is ₹150.

  $14(p-1) + 4(c+7) = 150$

Simplify the Second Equation

Expand and simplify Equation 2:

$14p - 14 + 4c + 28 = 150$

$14p + 4c + 14 = 150$

$14p + 4c = 150 - 14$

$14p + 4c = 136$

Divide the entire equation by 2 to simplify further:

$7p + 2c = 68 \quad \text{(Simplified Equation 2)}$

Solve the System of Equations

Now we have a system of two linear equations:

1. $7p + 8c = 230$
2. $7p + 2c = 68$

Subtract the simplified Equation 2 from Equation 1:

$(7p + 8c) - (7p + 2c) = 230 - 68$

$6c = 162$

Solve for $c$:

$c = \frac{162}{6} = 27$

Substitute the value of $c=27$ back into the simplified Equation 2 ($7p + 2c = 68$):

$7p + 2(27) = 68$

$7p + 54 = 68$

$7p = 68 - 54$

$7p = 14$

Solve for $p$:

$p = \frac{14}{7} = 2$

So, the original cost of a pen is ₹2 and the original cost of a pencil is ₹27.

Calculate the Final Cost

The question asks for the original cost of 8 pens and 8 pencils, which is $8p + 8c$.

$8p + 8c = 8(2) + 8(27)$

$= 16 + 216$

$= 232$

The original cost of 8 pens and 8 pencils is ₹232.