Question

The monthly income of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each save Rs. 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?

Answer 1

Let the income of Shyam = 3x
$\therefore$ Income of Bubban = 4x ($\because$ Income are in ratio of 3 : 4)
The experience of Shyam = 5y ($\because$ expenditure ratio 5 : 7)
The experience of Bubban = 7y
Saving of Shyam = 3x - 5y = 15000
Saving of Bubban = 4x - 7x = 15000
Putting in matrix form:
$\left[\begin{array}{cc}3& -5\\ 4& -7\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}15000\\ 15000\end{array}\right]$
or
$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{-21+20}\left[\begin{array}{cc}-7& 5\\ -4& 3\end{array}\right]\left[\begin{array}{c}15000\\ 15000\end{array}\right]=\left[\begin{array}{cc}-7& 5\\ -4& 3\end{array}\right]\left[\begin{array}{c}15000\\ 15000\end{array}\right]=\left[\begin{array}{c}30000\\ 15000\end{array}\right]\Rightarrow x=30000,y=15000$
$\therefore$ Income and expenditure of Shyam = 90,000 and 75,000\-
Income and expenditure of Bubban = 120,000 and 105,000\-