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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.
Solution
| 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 =
\[\left( 12 \times 40 \right) paise\]= Rs 4.80
Cost of pens per dozen =
\[Rs . \left( 12 \times 1 . 25 \right)\]= Rs 15
Cost ofpPencils per dozen =
\[\left( 12 \times 35 \right) paise\]= Rs 4.20
\[\therefore \begin{bmatrix}12 & 5 & 6 \\ 10 & 6 & 7 \\ 11 & 13 & 8\end{bmatrix}\begin{bmatrix}4 . 80 \\ 15 \\ 4 . 20\end{bmatrix} = \begin{bmatrix}12 \times 4 . 80 + 5 \times 15 + 6 \times 4 . 20 \\ 10 \times 4 . 80 + 6 \times 15 + 7 \times 4 . 20 \\ 11 \times 4 . 80 + 13 \times 15 + 8 \times 4 . 20\end{bmatrix}\]
\[ = \begin{bmatrix}57 . 60 + 75 + 25 . 20 \\ 48 + 90 + 29 . 40 \\ 52 . 80 + 195 + 33 . 60\end{bmatrix}\]
\[ = \begin{bmatrix}157 . 80 \\ 167 . 40 \\ 281 . 40\end{bmatrix}\]
Thus, the bills of A, B and C are Rs 157.80, Rs 167.40 and Rs 281.40, respectively.
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