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

Shopkeepers	Notebooks In dozen	Pens In dozen	Pencils In dozen
A	12	5	6
B	10	6	7
C	11	3	8

Here,
Cost of notebooks per dozen = $\left(12\times 40\right)\mathrm{paise}$ = Rs 4.80
Cost of pens per dozen = $\mathrm{Rs}.\left(12\times 1.25\right)$ = Rs 15
Cost ofpPencils per dozen = $\left(12\times 35\right)\mathrm{paise}$ = Rs 4.20

$$\begin{gathered} \therefore \left[\begin{array}{ccc}12& 5& 6\\ 10& 6& 7\\ 11& 13& 8\end{array}\right]\left[\begin{array}{c}4.80\\ 15\\ 4.20\end{array}\right]=\left[\begin{array}{c}12\times 4.80+5\times 15+6\times 4.20\\ 10\times 4.80+6\times 15+7\times 4.20\\ 11\times 4.80+13\times 15+8\times 4.20\end{array}\right] \\ =\left[\begin{array}{c}57.60+75+25.20\\ 48+90+29.40\\ 52.80+195+33.60\end{array}\right] \\ =\left[\begin{array}{c}157.80\\ 167.40\\ 281.40\end{array}\right] \end{gathered}$$

Thus, the bills of A, B and C are Rs 157.80, Rs 167.40 and Rs 281.40, respectively.