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.
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.
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