Two shops P and R sell pens and notebooks. The numbers sold in a day are given by the matrix \(Q = \begin{bmatrix}10&20\\15&10\end{bmatrix}\), where row 1 is shop P, row 2 is shop R, column 1 is pens and column 2 is notebooks. If x and y are the prices (in Rs.) of a pen and a notebook, and \(Q\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}400\\300\end{bmatrix}\) gives the money received by the two shops, then the price of a notebook is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 15
Multiplying row by column and using equality of matrices:
\(10x + 20y = 400\), that is \(x + 2y = 40\)
\(15x + 10y = 300\), that is \(3x + 2y = 60\)
Subtracting the first from the second,
\(2x = 20\), so \(x = 10\)
Then
\(10 + 2y = 40\)
\(y = 15\)
So a notebook costs Rs. 15 (and a pen Rs. 10).