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