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 = \(\begin{bmatrix} 3x \\[0.3em] 4x\end{bmatrix}\)

Expenditure Matrix = \(\begin{bmatrix} 5y \\[0.3em] 7y\end{bmatrix}\) 

Now, 

Saving = \(\begin{bmatrix} 3x \\[0.3em] 4x\end{bmatrix}\)- \(\begin{bmatrix} 5y \\[0.3em] 7y\end{bmatrix}\)

Given : 

Saving = 15000 each 

Therefore, we have,

\(\begin{bmatrix} 15000 \\[0.3em] 15000\end{bmatrix}\)= \(\begin{bmatrix} 3x \\[0.3em] 4x\end{bmatrix}\)- \(\begin{bmatrix} 5y \\[0.3em] 7y\end{bmatrix}\)

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

X = 25000. 

There monthly incomes are, 

3 x = 3 × 15000 = 45000 and 

4 x = 4 × 15000 = 60000.