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 ?
Get the complete, step-by-step math solution for: "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 pla...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
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 3×3 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 (SB). 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.