Q. 84.8( 4 Votes )

The monthly incom

Answer :

Given: Monthly incomes and monthly expenditures of Aryan and Babban are in the ratio 3:4 and 5:7 respectively.


To find: Their monthly incomes using the matrix method


Let the income of Aryan and Babban be 3x and 4x, and their expenditures are 5y and 7y


Income – Expenditure = Saving


Therefore,


3x – 5y = 15000


4x – 7y = 15000


To solve this equation and get values of x, y, we have:


AX = B where,




Now, check whether the system has a unique solution or not:



= 3 × -7 – 4 × (-5)


= -21 + 20


= -1


Since,


The system of the equation is consistent and have a unique solution


AX = B


X = A-1 B


Formula used:














Thus,




X = A-1 B








Solutions of the equations are x = 30000, y = 15000


The income of Aryan is 3x = 3 × 30000 = Rs. 90000


The income of Babban is 4x = 4 × 30000 = Rs. 120000


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