Question

A shopkeeper sells 50 Chemistry, 60 Physics and 35 Maths books on day I and sells 40 Chemistry, 45 Physics and 50 Maths books on day II. If the selling price for each subject book is \( \text{Rs } 150 \) (Chemistry), \( \text{Rs } 175 \) (Physics) and \( \text{Rs } 180 \) (Maths), then find his total sale in two days, using matrix method. If cost price of all the books together is \( \text{Rs } 35,000 \), what profit did he earn after the sale of two days?

Hint:

Quick Tip: When using the matrix method for calculating sales, ensure that each matrix represents a consistent set of quantities (e.g., quantities, prices). Matrix multiplication can simplify the process of calculating total sales.

Answer 1

Let matrices represent the number of books sold for each subject on Day I and Day II. Total sales are calculated by multiplying the price of each book by its quantity sold. The number of books sold on Day I is given by: \[ \mathbf{N}_1 = \begin{pmatrix} 50 \\ 60 \\ 35 \end{pmatrix} \] The number of books sold on Day II is given by: \[ \mathbf{N}_2 = \begin{pmatrix} 40 \\ 45 \\ 50 \end{pmatrix} \] The price of each book is given by: \[ \mathbf{P} = \begin{pmatrix} 150 \\ 175 \\ 180 \end{pmatrix} \] The total sales matrix is the sum of sales from Day I and Day II: \[ \mathbf{S} = \mathbf{N}_1^T \mathbf{P} + \mathbf{N}_2^T \mathbf{P} \] Performing matrix multiplication: \[ \mathbf{S} = \begin{pmatrix} 50 & 60 & 35 \end{pmatrix} \begin{pmatrix} 150 \\ 175 \\ 180 \end{pmatrix} + \begin{pmatrix} 40 & 45 & 50 \end{pmatrix} \begin{pmatrix} 150 \\ 175 \\ 180 \end{pmatrix} \] \[ \mathbf{S} = (50 \times 150 + 60 \times 175 + 35 \times 180) + (40 \times 150 + 45 \times 175 + 50 \times 180) \] \[ \mathbf{S} = (7500 + 10500 + 6300) + (6000 + 7875 + 9000) = 24300 + 22875 = 47175 \] The total sale over two days is Rs 47,175. The cost price for all books is Rs 35,000. The profit is calculated as: \[ \text{Profit} = \text{Total sale} - \text{Cost price} = 47175 - 35000 = 12175 \] The profit earned after two days of sales is Rs 12,175.