The cost of 2 pens and 5 pencils is ₹ 57. If the cost of a pen is increased by ₹ 1.50 and that of a pencil is decreased by ₹ 1, then the cost of 5 pens and 3 pencils is ₹ 109. What is the original cost of 3 pens and 4 pencils?

Correct option is C

​$$\textbf{Given:} \\2 \text{ pens} + 5 \text{ pencils} = 57 \\\text{Increase in cost of one pen} = 1.50 \\\text{Decrease in cost of one pencil} = 1 \\\text{New cost of } 5 \text{ pens and } 3 \text{ pencils} = 109 \\\textbf{Concept Used:} \\\text{Linear equations in two variables} \\\textbf{Formula Used:} \\ax + by = c \\\textbf{Solution:} \\\text{Let cost of one pen} = x \\\text{Let cost of one pencil} = y \\2x + 5y = 57 \quad (1) \\\text{New cost of one pen} = x + 1.5 \\\text{New cost of one pencil} = y - 1 \\5(x + 1.5) + 3(y - 1) = 109 \\5x + 7.5 + 3y - 3 = 109 \\5x + 3y = 104.5 \quad (2) \\\text{Multiply (1) by } 3: \\6x + 15y = 171 \quad (3) \\\text{Multiply (2) by } 5: \\25x + 15y = 522.5 \quad (4) \\(4) - (3): \\19x = 351.5 \\x = 18.5 \\\text{Substitute } x \text{ in (1):} \\2(18.5) + 5y = 57 \\37 + 5y = 57 \\y = 4 \\\text{Original cost of } 3 \text{ pens and } 4 \text{ pencils:} \\3x + 4y = 3(18.5) + 4(4) \\= 55.5 + 16 \\= 71.5 \\\textbf{Final Answer:} \\71.50$$​​