Rita purchased 9 pens and 7 pencils for ₹66. Megha also bought 5 pens and 11 pencils of the same kind for ₹58. What is the cost of 3 pencils?

₹9

The correct answer is Option (1) → ₹9

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

According to the question:

$9x + 7y = 66 \quad \text{(1)}$

$5x + 11y = 58 \quad \text{(2)}$

Multiply equation (1) by 5:

$45x + 35y = 330 \quad \text{(3)}$

Multiply equation (2) by 9:

$45x + 99y = 522 \quad \text{(4)}$

Subtract equation (3) from equation (4):

$(45x + 99y) - (45x + 35y) = 522 - 330$

$64y = 192$

$y = \frac{192}{64} = 3$

Now substitute $y = 3$ in equation (1):

$9x + 7(3) = 66$

$9x + 21 = 66$

$9x = 45$

$x = \frac{45}{9} = 5$

Therefore, cost of a pencil = $3$

Cost of 3 pencils = $3 \times 3 = 9$