Q. 114.5( 11 Votes )

# 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?

Answer :

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.

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