The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

To find the total amount the bookshop will receive from selling all the books using matrix algebra, we can represent the problem using matrices and perform matrix multiplication. Here’s how:

### Step 1: Define the quantities of the books in matrix form
Let \( Q \) be a row matrix representing the quantities of the books (in dozens):

\[
Q = \begin{bmatrix} 10 & 8 & 10 \end{bmatrix}
\]
Here:
- 10 dozen chemistry books
- 8 dozen physics books
- 10 dozen economics books

### Step 2: Define the prices of the books in matrix form
Let \( P \) be a column matrix representing the prices of the books (per book):

\[
P = \begin{bmatrix} 80 \\ 60 \\ 40 \end{bmatrix}
\]
Here:
- Rs. 80 per chemistry book
- Rs. 60 per physics book
- Rs. 40 per economics book

### Step 3: Calculate the total number of books
Since the quantities are in dozens, we convert them into units by multiplying each by 12:

\[
Q_{\text{units}} = 12 \times Q = \begin{bmatrix} 120 & 96 & 120 \end{bmatrix}
\]

### Step 4: Multiply the matrices
The total revenue from selling all the books can be found by multiplying the row matrix \( Q_{\text{units}} \) by the column matrix \( P \):

\[
\text{Total Revenue} = Q_{\text{units}} \times P
\]

Perform the multiplication:

\[
\text{Total Revenue} = \begin{bmatrix} 120 & 96 & 120 \end{bmatrix} \times \begin{bmatrix} 80 \\ 60 \\ 40 \end{bmatrix}
\]

### Step 5: Perform the calculation
The matrix multiplication will give us:

\[
\text{Total Revenue} = (120 \times 80) + (96 \times 60) + (120 \times 40)
\]

Now, calculate each term:

- \( 120 \times 80 = 9600 \)
- \( 96 \times 60 = 5760 \)
- \( 120 \times 40 = 4800 \)

Adding these together:

\[
\text{Total Revenue} = 9600 + 5760 + 4800 = 20160
\]

### Final Answer
The total amount the bookshop will receive from selling all the books is Rs. 20,160.

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Do you need any further details or have any questions about the process?

Here are some related questions to explore further:
1. How would the total revenue change if the price of physics books increases by 10%?
2. What would be the total revenue if the school decided to sell only half of the economics books?
3. How would you represent the problem if the prices of the books were given as a percentage discount?
4. How can matrix algebra be used to track inventory across multiple bookstores?
5. What if the number of books sold varied each day—how would you adjust the matrix multiplication?

**Tip:** When dealing with quantities in dozens or other groupings, remember to convert to individual units before performing any financial calculations!

Discover how to calculate the total revenue from selling 10 dozen chemistry books at Rs. 80 each, 8 dozen physics books at Rs. 60 each, and 10 dozen economics books at Rs. 40 each using matrix algebra. Follow a step-by-step solution to multiply matrices and find the total amount received by the bookshop.

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