The cost of 2 pencils and 3 pens is ₹55 and the cost of 7 pencils and 2 pens is ₹65. What is the total price (in ₹) of one pen and one pencil?

Cost of 2 pencils and 3 pens = ₹55

Cost of 7 pencils and 2 pens = ₹65

Algebraic Equations: Formulating and solving equations based on the given conditions.

As per the question;

2 pencils + 3 pens = 55 – (i)

7 pencils + 2 pens = 65 – (ii)

Multiply eq (i) with 2 and eq (ii) with 3

4 pencils + 6 pens = 110 – (iii)

21 pencils + 6 pens = 195 – (iv)

Subtracting Eq (iii) from eq (iv)

We get,

17 pencils = ₹85

1 pencil = ₹5

By eq (i)

2 × 5 + 3 pens = 55

1 pen = ₹15

So, the cost of 1 pen and 1 pencil = 5 + 15 = ₹20