Question

In a shop, the cost of 3 pens and 3 pencils is Rs. 9 and the cost of 4 pens and 6 pencils is Rs. 14. The cost of each pencil in Rs. is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

When two linear equations are given, always try to simplify the smaller equation first. This reduces substitution complexity and minimizes calculation errors in elimination problems.

Answer 1

The Correct Option is A

Concept: This problem is based on forming and solving a system of linear equations in two variables. Let the cost of one pen be \(x\) and the cost of one pencil be \(y\). We convert the given conditions into mathematical equations and solve them using substitution or elimination method.

Step 1: Forming the equations Let: \[ \text{Cost of one pen} = x, \quad \text{Cost of one pencil} = y \] From the first condition: \[ 3x + 3y = 9 \quad \cdots (A) \] From the second condition: \[ 4x + 6y = 14 \quad \cdots (B) \]

Step 2: Simplify Equation (A) Divide equation (A) by 3: \[ x + y = 3 \quad \cdots (C) \]

Step 3: Express one variable From equation (C): \[ x = 3 - y \quad \cdots (D) \]

Step 4: Substitute into Equation (B) Substitute \(x = 3 - y\) into equation (B): \[ 4(3 - y) + 6y = 14 \] Expanding: \[ 12 - 4y + 6y = 14 \] \[ 12 + 2y = 14 \] \[ 2y = 2 \] \[ y = 1 \] Thus, the cost of each pencil is: \[ \boxed{1} \]