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?
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.