The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3

• Linear Equations (C10)

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

Solution

Denote the incomes of the two person by 9x and 7x and their expenditures by 4y and 3y respectively.

Then the equations formed in the situation is given by:

9x – 4y = 2000 ... (1)

7x – 3y = 2000 ... (2)

Step 1: Multiply Equation (1) by 3 and Equation (2) by 4 to make the coefficients of y equal. Then you get the equations:

27x – 12y = 6000 ... (3)

28x – 12y = 8000 ... (4)

Step 2: Subtract Equation (3) from Equation (4) to eliminate y, because the coefficients of y are the same. So, you get

(28x – 27x) – (12y – 12y) = 8000 – 6000

x = 2000

Step 3: Substituting this value of x in (1),

9(2000) – 4y = 2000

y = 4000

The solution of the equations is x = 2000, y = 4000.

Therefore, the monthly incomes of the persons are Rs. 18,000 and Rs. 14,000, respectively.