This is the basic and conceptual question from linear equations in two variables in which we have to find the monthly income of a and b if their monthly expenditures ratio is given and it is also given that each saves 9000 per month.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 29

## Given ratio of incomes =5:4

And the ratio of their expenditures =7:5

Saving of each person = Rs. 3000

## Let incomes of two persons

=5x and 4x

And their expenditures =7y and 5y

According to the question, 5x−7y=3000…(i)

4x−5y=3000…( ii )

On multiplying Eq. (i) by 4 and Eq. (ii) by 5 to make the coefficients of x equal, we get

20x−28y=12000…( iii )

20x−25y=15000…( iv )

On subtracting Eq. (iii) from (iv), we get

20x−25y−20x+28y=15000−12000

⇒3y=3000

⇒y=1000

On putting the y=1000 in Eq. (i), we get

5x−7y=3000

⇒5x−7(1000)=3000

⇒5x=10000

⇒x=2000

Thus, monthly income of both the persons are 5(2000) and 4(2000) , i.e.

Rs. 10000 and Rs.8000