Q. 713.7( 4 Votes )

Three shopkeepers

Answer :

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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