Given the purchase details of three shopkeepers A, B and C.
A: 12 dozen notebooks, 5 dozen pens and 6 dozen pencils
B: 10 dozen notebooks, 6 dozen pens and 7 dozen pencils
C: 11 dozen notebooks, 13 dozen pens and 8 dozen pencils
Hence, the items purchased by A, B and C can be represented in matrix form with rows denoting the shopkeepers and columns denoting the number of dozens of items as –
The price of each of the items is also given.
Cost of one notebook = 40 paise
⇒ Cost of one dozen notebooks = 12 × 40 paise
⇒ Cost of one dozen notebooks = 480 paise
∴ Cost of one dozen notebooks = Rs 4.80
Cost of one pen = Rs 1.25
⇒ Cost of one dozen pens = 12 × Rs 1.25
∴ Cost of one dozen pens = Rs 15
Cost of one pencil = 35 paise
⇒ Cost of one dozen notebooks = 12 × 35 paise
⇒ Cost of one dozen notebooks = 420 paise
∴ Cost of one dozen notebooks = Rs 4.20
Hence, the cost of purchasing one dozen of the items can be represented in matrix form with each row corresponding to an item as –
Now, the individual bill for each shopkeeper can be found by taking the product of the matrices X and Y.
Thus, the bills of shopkeepers A, B and C are Rs 157.80, Rs 167.40 and Rs 281.40 respectively.
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