Question

Ramesh and Govind are two friends of a class. Ramesh wants to buy five pens and seven notebooks, Govind wants to buy three pens and ten notebooks. Both of them went to a shop. The price of one pen and one notebook which they have selected was Rs $ 5 $ and Rs $ 12 $ . Using matrix multiplication, find the amount required for each one of them

Answer 1

Hint: The given question is related to the concept of matrices. Here, we are given the quantity of pens and notebooks bought by both Ramesh and Govind, along with that we are given the price of one pen and one notebook. In order to solve this question, we will have to construct two matrices - one for the quantity and one for the price. Then, multiply those two matrices to get the required solution.

Complete step-by-step answer:
Given Ramesh wants to buy five pens and seven notebooks and Govind wants to buy three pens and ten notebooks. The cost of one pen is Rs $ 5 $ while the cost of one notebook is Rs $ 12 $ .
Let us solve this question, by constructing two matrices.
Let matrix A be of order $ 2 \times 2 $ representing the quantities of pens and notebooks.
 $ A = \left| {\begin{array}{*{20}{c}}
  5&7 \\
  3&{10}
\end{array}} \right| $
Here, column one represents the number of pens while column two represents the number of notebooks. Row one represents Ramesh while row two represents Govind.
Let matrix B be of order $ 2 \times 1 $ representing the price of each pen and notebook.
 $ B = \left| {\begin{array}{*{20}{c}}
  5 \\
  {12}
\end{array}} \right| $
Here, row one represents the price of one pen while row two represents the price of one notebook.
Now, we do matrix multiplication and get,
 $
  A \times B = \left| {\begin{array}{*{20}{c}}
  5&7 \\
  3&{10}
\end{array}} \right|\left| {\begin{array}{*{20}{c}}
  5 \\
  {12}
\end{array}} \right| \\
  A \times B = \left| {\begin{array}{*{20}{c}}
  {5\left( 5 \right) + 7\left( {12} \right)} \\
  {3\left( 5 \right) + 10\left( {12} \right)}
\end{array}} \right| \\
  A \times B = \left| {\begin{array}{*{20}{c}}
  {25 + 84} \\
  {15 + 120}
\end{array}} \right| \\
  A \times B = \left| {\begin{array}{*{20}{c}}
  {109} \\
  {135}
\end{array}} \right| \\
  $
Therefore, the amount required by Ramesh is Rs $ 109 $ while the amount required by Govind is Rs $ 135 $ .
So, the correct answer is “Rs $ 135 $ ”.

Note: The given question was an application-based question of matrix multiplication. Students often tend to make mistakes while multiplication of the two matrices. They should avoid making such mistakes. Similar types of questions can be practised for more clarity and better understanding.