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

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: \[ {1} \]