Question

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 2000 per month .find the monthly incomes.

Answer 1

let the incomes be 9x and 7x respectively.
And let the expenditures be 4y and 3y.

Income-expenditure=saving
ATQ:9x-4y=2000.......eqn 1
7x-3y=2000.....eqn 2

There are two variables and two eqns.
solve it and get the value of x and y.
monthly income wud be 9x and 7x.
done.

Answer 2

$<b><i>$
$<u>Answer :</u>$

Let the monthly incomes be represented by x and their expenditure be represented by y.

According to the given income ratios,

Income of the first person is 9x and that of the second persons is 7x.

$<u>According to the given expenditure ratios;</u>$

Expenditure of the first person is 4y and the second person’s is 3y.

Both of them manage to save ₹2000 per month.

i.e. income – expenditure = savings

Then,

9x – 4y = 2000 …I

7x - 3y = 2000 …II

Multiplying I by 3 and II by 4, we get

27x – 12y = 6000 …III

28x – 12y = 8000 …IV

Subtracting III from IV, we get

x = 2000

Putting x = 2000 in I we get,

18000 – 4y = 2000

⇒ 16000 = 4y

⇒ y = 4000

Now,

$<u>Income of the first person = 9x = 9× 2000 = 18000</u>$

$<u>Income of the second person = 7x = 7× 2000 = 14000</u>$