Question

The book shop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the book shop will receive from selling all the books using matrix algebra.
(a) Rs 20,160
(b) Rs 20,150
(c) Rs 20,170
(d) Rs 20,180

Answer 1

Hint: We will use the matrix method here. Suppose that we consider the matrices as $\left[ a\,\,b \right]$ and $\left[ \begin{align}
  & c \\
 & d \\
\end{align} \right]$. Then, the multiplication of the matrices $\left[ a\,\,b \right]$ and $\left[ \begin{align}
  & c \\
 & d \\
\end{align} \right]$ will be like so, $\left[ a\,\,b \right]\left[ \begin{align}
  & c \\
 & d \\
\end{align} \right]=a\times c+b\times d$. With the help of this matrix method we are going to solve the question to get the desired answer.

Complete step-by-step answer:
As we know that 1 dozen means 12 units of anything. Therefore we will first convert the dozen into simple units. We will do this as 10 dozen chemistry books means $10\times 12$ chemistry books. Thus we get 120 chemistry books. Similarly, 8 dozen physics books means $8\times 12$ physics books which are 96 in number and 10 dozen economics books means $10\times 12$ economics books which is actually 120 economics books. We are also given the prices for the book as Rs. 80 for chemistry, Rs. 60 for physics and Rs. 40 for economics.
Now we will convert the given information into matrix form. This can be done by diving number of books in one matrix and the other book in the second matrix. We will form the matrices in such a way that we will get the product of numbers of books along with the prices of the books. This can be done by forming the matrix of number of books as $\left[ 120\,\,\,\,96\,\,\,\,120 \right]$ and their respected prices as $\left[ \begin{align}
  & 80 \\
 & 60 \\
 & 40 \\
\end{align} \right]$. After multiplying these matrices together we will get,
 $\left[ 120\,\,\,\,96\,\,\,\,120 \right]\left[ \begin{align}
  & 80 \\
 & 60 \\
 & 40 \\
\end{align} \right]=\left[ 120\times 80+96\times 60+120\times 40 \right]$
$\Rightarrow \left[ 120\,\,\,\,96\,\,\,\,120 \right]\left[ \begin{align}
  & 80 \\
 & 60 \\
 & 40 \\
\end{align} \right]=\left[ 9600+5760+4800 \right]$
$\Rightarrow \left[ 120\,\,\,\,96\,\,\,\,120 \right]\left[ \begin{align}
  & 80 \\
 & 60 \\
 & 40 \\
\end{align} \right]=20160$
Therefore, the total amount the book shop will receive from selling all the books is Rs. 20160. Hence, the correct option is (a).

Note: We have solved this question by matrix algebra because it was strictly said in the question to use it. Remember to not form the matrix in the form $\left[ \begin{align}
  & 120 \\
 & 96 \\
 & 120 \\
\end{align} \right]\left[ 80\,\,\,60\,\,\,40 \right]$ otherwise we will get the matrix like this $\left[ \begin{align}
  & 9600\,\,\,7200\,\,\,4800 \\
 & 7680\,\,\,5760\,\,\,3840 \\
 & 9600\,\,\,7200\,\,\,4800 \\
\end{align} \right]$. And after this we need to add the diagonals in order to get the solution which is not acceptable because we have to explain then why we are ignoring the rest of the numbers.