Q. 114.5( 11 Votes )

The monthly incomes of Aryan and Babban are in the ration 3: 4 and their monthly expenditures are in the ratio 5: 7. If each saves 15000 per month, find their monthly incomes using the matrix method. This problem reflects which value?

Answer :

Let us represent the situation through a matrix.


We will make two matrices: Income and Expenditure Matrices.


We know that Saving = Income – Expenditure.


Let the incomes of Aryan and Babban be 3x and 4x respectively and the expenditures be 5y and 7y respectively.


Income Matrix =


Expenditure Matrix =


Now, Saving =


Given: Saving = 15000 each


Therefore, we have,



So,


3 x – 5 y = 15000 ….(1)


4 x – 7 y = 15000 …..(2)


Solving equations 1 and 2, we get,


Multiplying eq(1) by 4 and eq(2) by 3 we get,


12 x – 20 y = 60000 ….(3)


12 x – 21 y = 45000 …..(4)


Eq(3) – Eq(4),


Y = 15000


Putting this value in eq(1) we get,


3 x – 4 × 15000 = 15000


3 x = 75000


X = 25000.


There monthly incomes are, 3 x = 3 × 15000 = 45000 and


4 x = 4 × 15000 = 60000.

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