Question

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

Answer 1

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.

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