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

Question

Philoid · Accepted Answer

Let the monthly incomes of Aryan and Babbar be 3x and 4x respectively.

Let their monthly expenditures be 5y and 7y respectively.

Given that both of them save Rs 15000 per month.

We know that the savings is the difference between the income and the expenditure.

Thus, we have two equations –

3x – 5y = 15000

4x – 7y = 15000

Recall that the solution to the system of equations that can be written in the form AX = B is given by X = A^-1B.

Here,

We know the inverse of a matrix is given by

|A| = (3)(–7) – (4)(–5) = –21 + 20 = –1

We have X = A^–1B.

Monthly income of Aryan = 3x = 3 × Rs 30000 = Rs 90000

Monthly income of Babbar = 4x = 4 × Rs 30000 = Rs 120000

Thus, the monthly incomes of Aryan and Babbar are Rs 90000 and Rs 120000 respectively.

This problem tells us that savings are important and our income must not be spent wastefully.