[CBSE 2025] The monthly incomes of two persons are in the ratio is 9:7 . . .

Question : The monthly incomes of two persons are in the ratio is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save ₹ 5,000 per month, express the given situation algebraically as a system of linear equations in two variables. Hence, find their respective monthly incomes.

CBSE 2025

Solution : 

Let the monthly income of the two persons be 9x and 7x respectively and their monthly expenditures be 4y and 3y respectively. 

ATQ

9x-4y=5000 — (1) 
7x-3y=5000 — (2) 

[9x-4y=5000 ] × 3
[7x-3y=5000 ] × 4

27x-12y=15000 
28x-12y=20000
-     +      -   
--------------------
-x + 0 = -5000
--------------------

-x=-5000
x=5000

Month incomes of two persons 
9x = 9×5000 = 45000

7x = 7×5000 = 35000

Hence, monthly income of two persons are ₹45,000 and ₹ 35,000 respectively.