Class CBSE Class 12 Mathematics Matrices and Determinants Q #1475
COMPETENCY BASED
REMEMBER
3 Marks 2025 AISSCE(Board Exam) SA
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 such subject book is ₹150 (Chemistry), ₹175 (Physics) and ₹180 (Maths), then find his total sale in two days, using matrix method. If cost price of all the books together is ₹35,000, what profit did he earn after the sale of two days?
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Detailed Solution

Step 1: Represent the book sales in matrix form

Let matrix $A$ represent the number of books sold on each day for each subject. $$A = \begin{bmatrix} 50 & 60 & 35 \\ 40 & 45 & 50 \end{bmatrix}$$ Here, rows represent Day I and Day II, and columns represent Chemistry, Physics, and Maths respectively.

Step 2: Represent the selling prices in matrix form

Let matrix $B$ represent the selling price of each book. $$B = \begin{bmatrix} 150 \\ 175 \\ 180 \end{bmatrix}$$ Here, rows represent the selling price of Chemistry, Physics, and Maths books respectively.

Step 3: Calculate the total sales for each day

To find the total sales for each day, we multiply matrix $A$ by matrix $B$. $$AB = \begin{bmatrix} 50 & 60 & 35 \\ 40 & 45 & 50 \end{bmatrix} \begin{bmatrix} 150 \\ 175 \\ 180 \end{bmatrix} = \begin{bmatrix} (50 \times 150) + (60 \times 175) + (35 \times 180) \\ (40 \times 150) + (45 \times 175) + (50 \times 180) \end{bmatrix}$$ $$AB = \begin{bmatrix} 7500 + 10500 + 6300 \\ 6000 + 7875 + 9000 \end{bmatrix} = \begin{bmatrix} 24300 \\ 22875 \end{bmatrix}$$ The total sale on Day I is ₹24,300 and on Day II is ₹22,875.

Step 4: Calculate the total sale in two days

The total sale in two days is the sum of the sales on Day I and Day II. Total Sale = ₹24,300 + ₹22,875 = ₹47,175

Step 5: Calculate the profit

The cost price of all books is ₹35,000. Profit = Total Sale - Cost Price Profit = ₹47,175 - ₹35,000 = ₹12,175

Final Answer: Total sale in two days is ₹47,175 and the profit is ₹12,175.

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Pedagogical Audit
Bloom's Analysis: This is an REMEMBER question because the student needs to recall the concept of matrix multiplication and apply it to solve the problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to apply the procedure of matrix multiplication to find the total sales and then calculate the profit.
Syllabus Audit: In the context of CBSE Class 12, this is classified as Application. The question involves applying the concept of matrices to a real-world problem, which is a competency-based application of the topic.

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