Question
A cooperative store has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are ₹8.30, ₹3.45 and ₹4.50 respectively. Find the total amount received using matrix method.
Solution
Step 1: Convert to Matrix Form
Quantity (in dozens):
\[ Q = \begin{bmatrix} 10 & 8 & 5 \end{bmatrix} \]Price per book:
\[ P = \begin{bmatrix} 8.30 \\ 3.45 \\ 4.50 \end{bmatrix} \]Step 2: Convert Dozens into Units
\[ 1 \text{ dozen} = 12 \] \[ Q = \begin{bmatrix} 120 & 96 & 60 \end{bmatrix} \]Step 3: Multiply
\[ \text{Total Amount} = Q \times P \] \[ = \begin{bmatrix} 120 & 96 & 60 \end{bmatrix} \begin{bmatrix} 8.30 \\ 3.45 \\ 4.50 \end{bmatrix} \]Step 4: Calculate
\[ = 120×8.30 + 96×3.45 + 60×4.50 \] \[ = 996 + 331.2 + 270 \] \[ = 1597.2 \]Final Answer
\[
\text{Total Amount} = ₹1597.20
\]