Question

The cost of 3 notebooks and 5 pens is ₹ 265. The cost of 2 notebooks and 9 pens is ₹ 205. Find the cost of one notebook and cost of one pen.

Answer 1

Given:

• The cost of 3 notebooks and 5 pens is ₹ 265.
• The cost of 2 notebooks and 9 pens is ₹ 205.

Let the cost of one notebook be ₹ x and the cost of one pen be ₹ y.

Step-wise calculation:

1. Write the equations from the given data: 

3⁢x + 5y = 265 

2x + 9y = 205

2. Multiply the first equation by 2 and the second equation by 3 to eliminate x after subtraction:

6x + 10y = 530   ...(3x + 5y = 265 × 2) 

6x + 27y = 615   ...(2x + 9y = 205 × 3) 

3. Subtract the first new equation from the second: 

(6x + 27y) – (6x + 10y) = 615 – 530 

17y = 85

⇒ y = 5

4. Substitute (y = 5) into the first original equation: 

3x + 5(5) = 265

⇒ 3x + 25 = 265

⇒ 3x = 240

⇒ x = 80

Cost of one notebook = ₹ 80.

Cost of one pen = ₹ 5.