Question

The sum of the cost of one Economic book, one Co-operation book and one account book is ₹ 420. The total cost of an Economic book, 2 Co-operation books and an Account book is ₹ 480. Also the total cost of an Economic book, 3 Co-operation books and 2 Account books is ₹ 600. Find the cost of each book using matrix method.

Answer 1

Let the cost of one economic book, one co-operation book and one account book be ₹ x, ₹ y and ₹ z respectively.

According to the first condition,

x + y + z = 420

According to the second condition,

x + 2y + z = 480

According to the third condition,

x + 3y + 2z = 600

Matrix form of the above system of equations is

`[(1, 1, 1),(1, 2, 1),(1, 3, 2)][(x), (y), (z)] = [(420), (480), (600)]`

Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁, we get

`[(1, 1, 1),(0, 1, 0),(0, 2, 1)][(x), (y), (z)] = [(420), (60), (180)]`

Applying R₃ → R₃ – 2R₂, we get

`[(1, 1, 1),(0, 1, 0),(0, 0, 1)][(x), (y), (z)] = [(420), (60), (60)]`

Hence, the original matrix is reduced to an upper triangular matrix.

∴ `[(x + y + z),(0 + y + 0),(0 + 0 + z)] = [(420), (60), (60)]`

∴ By equality of matrices, we get

x + y + z = 420  ...(i)

y = 60

z = 60

Substituting y = 60 and z = 60 in equation (i), we get

x + 60 + 60 = 420

∴ x = 420 – 120 = 300

∴ The cost of one economic book is ₹ 300, one co-operation book is ₹ 60 and one account book is ₹ 60.