Raman purchases 2 pens and 3 pencils and pays ₹36 to the shopkeeper. Her friend Siya purchases 3 pens and 2 pencils and pays ₹49. What is the cost of one pen?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹15
Let one pen cost ₹\(x\) and one pencil ₹\(y\). The two purchases give two equations; adding and subtracting them is quicker here because the numbers 2 and 3 appear crosswise.
Raman’s purchase: \(2x+3y=36\) (1)
Siya’s purchase: \(3x+2y=49\) (2)
Adding (1) and (2): \(5x+5y=85\), so \(x+y=17\) (3)
Subtracting (1) from (2): \(x-y=13\) (4)
Adding (3) and (4), the \(y\) terms cancel: \(2x=30\), so \(x=15\): one pen costs ₹15