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?

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**Solution:**

1. Let the cost of one pencil be *x* and one pen be *y*.

2. From the problem, we have two equations:
   - $2x + 3y = 55$  (i)
   - $7x + 2y = 65$  (ii)

3. Multiply equation (i) by 2 and equation (ii) by 3 to eliminate *y*:
   - $4x + 6y = 110$  (iii)
   - $21x + 6y = 195$  (iv)

4. Subtract equation (iii) from (iv):
   - $(21x + 6y) - (4x + 6y) = 195 - 110$
   - $17x = 85$
   - $x = \frac{85}{17} = 5$

5. Substitute $x=5$ into equation (i):
   - $2(5) + 3y = 55$
   - $10 + 3y = 55$
   - $3y = 45$
   - $y = 15$

6. Total cost of one pencil and one pen:
   - $x + y = 5 + 15 = 20$

**Answer:** ₹20

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