CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q364 Marksmatrix_multiplication
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 36 (Matrices)
Dealers P and Q sell motorcycle types A and B. In 2022 P sold 160 A and 70 B; Q sold 100 A and 40 B. In 2023 P sold 300 A and 150 B; Q sold 200 A and 60 B.
Part (1) 1 Marks
Write the 2022 sales matrix, with dealers as rows and types as columns.
Answer: [[160,70],[100,40]].
- Use row order P,Q and column order A,B.
- Place the four sales counts in their corresponding entries.
Part (2) 1 Marks
Write the corresponding 2023 sales matrix.
Answer: [[300,150],[200,60]].
- Keep the same row and column order.
- The rows are (300,150) and (200,60).
Part (3) 2 Marks
Using matrices, find each dealer’s 2022 profit if unit profits are ₹30000 for A and ₹20000 for B.
Answer: P ₹6200000, Q ₹3800000.
- Multiply the 2022 matrix by (30000,20000)ᵀ.
- The products are 160·30000+70·20000 and 100·30000+40·20000.
- These give ₹6200000 and ₹3800000.
Part (4) 2 Marks
Using matrices, find each dealer’s 2023 profit if unit profits are ₹40000 for A and ₹30000 for B.
Answer: P ₹16500000, Q ₹9800000.
- Multiply the 2023 matrix by (40000,30000)ᵀ.
- The products are 300·40000+150·30000 and 200·40000+60·30000.
- These give ₹16500000 and ₹9800000.