the monthly incomes of aryan and babban are in the ratio 3:4 and their monthly expenditure are in the ratio - Maths -

Question

the monthly incomes of aryan and babban are in the ratio 3:4 and
their monthly expenditure are in the ratio 5:7 if each saves Rs
15000 per month,find their monthly incomes using matrix method

Varun.Rawat · Accepted Answer

Let the
monthly incomes of Aryan and Babban be 3x and
4x,
respectively

Suppose
their monthly expenditures are 5y and 7y,
respectively

Since
each saves Rs 15,000 per month,

Monthly saving of Aryan: 3x-5y=15,000Monthly saving of Babban: 4x-7y=15,000

The above
system of equations can be written in the matrix form as
follows:
â€‹
3-54-7xy=1500015000

or,
AX = B,
where
A=3-54-7, X=xy and B=1500015000

Now,

A=3-54-7=-21--20=-1

Adj
A=-7-453T=-75-43

So,
A-1=1AadjA=-1-75-43=7-54-3

∴X=A-1B⇒xy=7-54-31500015000⇒xy=105000-7500060000-45000⇒xy=3000015000⇒x=30,000 and y=15,000

Therefore,

Monthly
income of Aryan =
3×Rs 30,000=Rs 90,000

Monthly
income of Babban =
4×Rs 30,000= Rs 1,20,000

the monthly incomes of aryan and babban are in the ratio 3:4 and their monthly expenditure are in the ratio 5:7 . if each saves Rs 15000 per month,find their monthly incomes using matrix method.