Question

The cost of 5 pens and 8 notebooks is ₹160, whereas the cost of 9 pens and 6 notebooks is ₹162. Find the cost of each.

Answer 1

Here, let:

Cost of one pen = ₹x

Cost of one notebook = ₹y

Given:

5x + 8y = 160     ...(1)

9x + 6y = 162     ...(2)

Multiply the equations to equalize the coefficients of one variable:

Multiply (1) by 3:

3(5x + 8y) = 3(160)

15x + 24y = 480     ...(3)

Multiply (2) by 4:

4(9x + 6y) = 4(162)

36x + 24y = 648     ...(4)

Subtracting equation (4) from equation (3):

(36x + 24y) − (15x + 24y) = 648 − 480

36x − 15x = 168

21x = 168

x = `168/21`

∴ x = 8

Substitute x = 8 into equation (1):

5(8) + 8y = 160

40 + 8y = 160

8y = 160 − 40

8y = 120

y = `120/8`

∴ y = 15

Hence, the cost of one pen is ₹8 and the cost of one notebook is ₹15.