The ratio of incomes of two persons is 9:7, and the ratio of their expenditure is 4:3. If each of them manages to save $2000 per month, find their monthly expenditure?

The correct answer is: $16000, $12000

Let their salaries be 9x and 7x.
Let their expenditure be 4y and 3y.
According to the question,
9x−4y=2000 —(1)
7x−3y=2000 —(2)
From (1)
x= 2000+4y/9 —(3)
On putting x in (2), we get
7× (2000+4y)/9−3y=2000
(14000+28y)/9−3y=2000
14000+28y−27y/9 =2000
14000+y=18000
y=4000
Now, put y in (3)
x= 2000+4×4000/9
x= 2000+16000/9
​x= 18000/9
x=2000
So,
Salary of first person =9×2000=Rs. 18000
Salary of second person =7×2000=Rs. 14000