Class 12 Matrices · Case Study4 Marksmatrix_applications
Class 12 Maths · Matrices · Case Study #32
Schools DPS, CVC and KVS organize a charity fair for flood relief. They sell handmade fans, mats and plates from recycled materials at selling prices ₹25, ₹100 and ₹50 each respectively. Quantities sold are given in the attached table.
Part (1) 2 Marks
Find the total amount collected by the three schools, using matrices.
Answer: ₹21,000
- Use schools as rows and products as columns: Q=[[40,50,20],[25,40,30],[35,50,40]], with price column p=[25,100,50]ᵀ.
- The row products Qp give [1000+5000+1000,625+4000+1500,875+5000+2000]ᵀ=[7000,6125,7875]ᵀ.
- The combined collection is ₹(7000+6125+7875)=₹21,000.
Part (2) 2 Marks
If the numbers of handmade fans and plates are interchanged for every school, find the new combined collection.
Answer: ₹21,250
- Swap the fan and plate columns to form Q′=[[20,50,40],[30,40,25],[40,50,35]]. Selling prices remain [25,100,50]ᵀ.
- The new row products are [500+5000+2000,750+4000+1250,1000+5000+1750]ᵀ=[7500,6000,7750]ᵀ.
- The new combined collection is ₹(7500+6000+7750)=₹21,250.