Example 11 - Chapter 3 Class 12 Matrices

Transcript

Example 11 (i) Two farmers Ramkishan and Gurcharan Singh cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in Rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B. September Sales (in Rupees) Basmati Permal Naura A = [■8(10,000&20,000&30,000@50,000&30,000&10,000)] October Sales (in Rupees) Basmati Permal Naura B = [■8(5000&10,000&6000@20,000&10,000&10,000)] (i) Find the combined sales in September and October for each farmer in each variety. Combined sales in September and October will be A + B A + B = [■8(10,000&20,000&30,000@50,000&30,000&10,000)] + [■8(5000&10,000&6000@20,000&10,000&10,000)] = [■8(10000+5000&20000+10000&30000+6000@50000+20000&30000+ 10,000&10000+10000)] = [■8(𝟏𝟓,𝟎𝟎𝟎&𝟑𝟎,𝟎𝟎𝟎&𝟑𝟔,𝟎𝟎𝟎@𝟕𝟎,𝟎𝟎𝟎&𝟒𝟎,𝟎𝟎𝟎&𝟐𝟎,𝟎𝟎𝟎)] Hence, Total Sales = [■8(15,000&30,000&36,000@70,000&40,000&20,000)] Example 11 (ii) Two farmers Ramkishan and Gurcharan Singh cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in Rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B. September Sales (in Rupees) Basmati Permal Naura A = [■8(10,000&20,000&30,000@50,000&30,000&10,000)] October Sales (in Rupees) Basmati Permal Naura B = [■8(5000&10,000&6000@20,000&10,000&10,000)] (ii) Find the decrease in sales from September to October. Decrease in sales from September to October will be A – B A – B = [■8(10,000&20,000&30,000@50,000&30,000&10,000)] – [■8(5000&10,000&6000@20,000&10,000&10,000)] = [■8(10000−5000&20000−10000&30000−6000@50000−20000&30000−10,000&10000−10000)] = [■8(𝟓𝟎𝟎𝟎&𝟏𝟎,𝟎𝟎𝟎&𝟐𝟒,𝟎𝟎𝟎@𝟑𝟎,𝟎𝟎𝟎&𝟐𝟎,𝟎𝟎𝟎&𝟎)] Hence, Decrease in sales from September to October = [■8(5000&10,000&24,000@30,000&20,000&0)] Example 11 (iii) Two farmers Ramkishan and Gurcharan Singh cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in Rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B. September Sales (in Rupees) Basmati Permal Naura A = [■8(10,000&20,000&30,000@50,000&30,000&10,000)] October Sales (in Rupees) Basmati Permal Naura B = [■8(5000&10,000&6000@20,000&10,000&10,000)] (iii) If both farmers receive 2% profit on gross sales, compute the profit for each farmer and for each variety sold in October. Profit = 2% × (Sales on October) = 2/100 × B = 0.02 × B = 0.02 × [■8(𝟓𝟎𝟎𝟎&𝟏𝟎,𝟎𝟎𝟎&𝟔𝟎𝟎𝟎@𝟐𝟎,𝟎𝟎𝟎&𝟏𝟎,𝟎𝟎𝟎&𝟏𝟎,𝟎𝟎𝟎)] = [■8(0.02×5000&0.02×10,000&0.02×6000@0.02×20,000&0.02×10,000&0.02×10,000)] = [■8(100&200&120@400&200&200)] Hence, Profit = [■8(100& 200& 120@400& 200& 200)] Hence, Ramkishan receives Rs 100 profit on sale of Basmati rice , Rs 200 profit on sale of Permal & Rs 120 profit in the sale of Naura in the month of October Hence, Gurcharan Singh receives Rs 400 profit on sale of Basmati rice , Rs 200 profit on sale of Permal & Rs 200 profit in the sale of Naura in the month of October