Three schools A, B and C organised a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand-made fans, mats and plates from recycled material at a cost of ₹ 25, ₹ 50 and ₹ 10 each respectively. The number of articles sold are given below : | School Articles | A | B | C | |---|---|---|---| | Hand-made fans | 50 | 30 | 35 | | Mats | 60 | 35 | 40 | | Plates | 40 | 50 | 25 | Based on the above information, answer the following questions : (i) What is the price matrix ? (ii) What is the sales matrix ? (iii) (a) What is the matrix of funds collected by School B ? OR (iii) (b) What is the total amount of funds collected by Schools A and C ?

Step 1: Formulate the Price Matrix

The problem states the cost of hand-made fans, mats, and plates are ₹ 25, ₹ 50, and ₹ 10 respectively. We can represent these prices as a row matrix, where each element corresponds to the price of an article.

Step 2: Formulate the Sales Matrix

The sales data is given in a table. We can represent this data as a $3 \times 3$ matrix, where rows represent the articles (fans, mats, plates) and columns represent the schools (A, B, C).

Step 3: Calculate Funds Collected by School B

To find the funds collected by School B, we multiply the price matrix $P$ by the column vector representing the sales of School B ($S_B$). This involves multiplying corresponding prices by the number of items sold and summing the results.

Step 4: Compute Funds Collected by School B

Performing the multiplication and summation, we find that School B collected ₹ 3000.

Step 5: Calculate Funds Collected by School A and C

Alternatively, to find the total funds collected by Schools A and C, we first calculate the funds collected by each school individually using matrix multiplication, similar to School B. Then, we sum these amounts.

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