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?

₹15

Raman purchases 2 pens and 3 pencils for ₹36: 2x+3y =36

Siya purchases 3 pens and 2 pencils for ₹49: 3x+2y =49

Now, we have a system of linear equations:

2x+ 3y =36

3x+2y =49

Multiply the first equation by 3 and the second equation by 2:

This gives us:

6x+9y = 108

6x+4y = 98

Next, subtract the second equation from the first to eliminate x

(6x +9y) − (6x +4y) = 108−98

5y =10

y = 2

Now that we have y =2, we can substitute this value into 2x+ 3y=36

2x +3(2) = 36

2x +6 = 36

x =15