We are given the following information:

1. The cost of 4 pens and 6 pencils is Rs 172.
2. The cost of 2 pens and 2 pencils is Rs 74.

Let the cost of 1 pen be $x$ and the cost of 1 pencil be $y$.

From the information given, we can form two equations:

1. $4x + 6y = 172$ (Equation 1)
2. $2x + 2y = 74$ (Equation 2)

Solving the system of equations:

First, simplify Equation 2 by dividing through by 2:

$x + y = 37 \quad \text{(Equation 3)}$

Now, substitute $x = 37 - y$ from Equation 3 into Equation 1:

$4(37 - y) + 6y = 172$

Expanding this equation:

$148 - 4y + 6y = 172$

Simplify:

$148 + 2y = 172$

Now, subtract 148 from both sides:

$2y = 24$

Solve for $y$:

$y = \frac{24}{2} = 12$

Thus, the cost of 1 pencil is Rs 12.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What is the cost of one pen?
2. How do you solve linear equations with two variables?
3. Can you solve for the total cost of 3 pens and 5 pencils now?
4. What is the graphical representation of these equations?
5. How do substitution and elimination methods compare in solving such problems?

Tip: When solving simultaneous equations, substitution is often simpler when one variable can easily be isolated from one of the equations.