the ratio of income of two persons is 9:7and the ratio of their expenditures is 4:3. if each of them manages to save ₹ 2000 per month, find their monthly incomes.
Answers
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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