Three shopkeepers

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.