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

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