Question

Three shopkeepers, A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs 1.25 and a pencil costs 35 paise. 

Use matrix multiplication to calculate each individual’s bill.

Answer 1

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 –

X =\(\begin{bmatrix} 12 & 5 & 6 \\[0.3em] 10 & 6 & 7 \\[0.3em] 11 & 13 & 8 \end{bmatrix}\)

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 –

Y =\(\begin{bmatrix} 4.80 \\[0.3em] 15 \\[0.3em] 4.20 \end{bmatrix}\)

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.