A stationery shop sells pens, notebooks and files. The numbers sold on Monday and Tuesday are given by the matrix \(S\), and the selling prices (in Rs.) per pen, per notebook and per file are given by the matrix \(P\):
\(S = \begin{bmatrix} 10 & 6 & 4 \\ 8 & 12 & 5 \end{bmatrix}\) (rows: Monday, Tuesday; columns: pens, notebooks, files), \(\quad P = \begin{bmatrix} 15 \\ 40 \\ 25 \end{bmatrix}\)
Using matrix multiplication, the total sales revenue of the shop for the two days together is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 1,215
Each row of S times the price column P gives the revenue of that day, so SP is a \(2 \times 1\) matrix:
\( \displaystyle SP = \begin{bmatrix} 10 \times 15 + 6 \times 40 + 4 \times 25 \\ 8 \times 15 + 12 \times 40 + 5 \times 25 \end{bmatrix} \)
\( \displaystyle SP = \begin{bmatrix} 150 + 240 + 100 \\ 120 + 480 + 125 \end{bmatrix} = \begin{bmatrix} 490 \\ 725 \end{bmatrix} \)
Monday’s revenue is Rs. 490 and Tuesday’s is Rs. 725. The total for the two days is
\(490 + 725 = 1215\)
So the total revenue is Rs. 1,215.