Question

the ratio income of two person is 9:7 and the ratio of their of theri expanditure is 4:3 if each of them manages to save 2000 per month per month find thier monthly income

Answer 1

Hey

Here is your answer,

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.

Hope it helps you!