Question

Two pens and three pencils cost Rs 86. Four pens and a pencil cost Rs. 112. Find the cost of a pen.

• A. \( \text{Rs. 20} \)
• B. \( \text{Rs. 10} \)
• C. \( \text{Rs. 25} \)
• D. \( \text{Rs. 15} \)
• E.

Hint:

For solving such problems, use substitution or elimination methods to form a system of linear equations and solve step by step.

Answer 1

The Correct Option is C

Let the cost of a pen be \( p \) and the cost of a pencil be \( q \). From the given conditions: \[ 2p + 3q = 86 \quad \text{(Equation 1)} \] \[ 4p + q = 112 \quad \text{(Equation 2)} \] Multiplying Equation 2 by 3: \[ 12p + 3q = 336 \] Now subtract Equation 1 from this: \[ (12p + 3q) - (2p + 3q) = 336 - 86 \] \[ 10p = 250 \quad \Rightarrow \quad p = 25 \] Thus, the cost of a pen is Rs. 25.