Question

22.
The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3.
If each of them saves 2000 per month, find their monthly incomes.
htninod nither hy multinlying the sum of the digits by 8 and​

Answer 1

Given :

The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them saves 2000 per month.

To find :

• Monthly incomes

Solution :

Let the income be x & expenditures be y

• Income and expenditure of first person = 9x and 4y

• Income and expenditure of second person = 7x and 3y

According to question

• Income - expenditure = saving

In the case of first person

→ 9x - 4y = 2000 ---(i)

In the case of second person

→ 7x - 3y = 2000 ----(ii)

Multiply (i) by 3 and (ii) by 4

• 27x - 12y = 6000
• 28x - 12y = 8000

Subtract both the equations

→ 27x - 12y - (28x - 12y) = 6000 - 8000

→ 27x - 12y - 28x + 12y = - 2000

→ 27x - 28x = - 2000

→ - x = - 2000

→ x = Rs.2000

•°• Income of first person = 9x = Rs.18000

•°• Income of 2nd person = 7x = Rs.14000

________________________________

Answer 2

GIVEN :

the ratio of incomes of two persons = 9:7

the ratio of expenditure of two persons=4:3

TO FIND :

Monthly incomes

NOW,

Let the income be x and expenditure be y

Income,expenditure of 1st person=9x and 4y

Income,expenditure of 2nd person=7x and 3y

ATQ (according to the Question)

Income - expenditure = saving

FIRST PERSON :

9x- 4y = 2000. (1)

SECOND PERSON :

7x- 3y = 3000. (2)

Multiply (1) by 3 and (2) by 4

→ 27x- 12y = 6000

→ 28x- 12y = 8000

Subtract both equations

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

27x- 12y-28x+12y = -2000

27x-28x = -2000

-x = -2000

x = 2000

» Income of first person= 9x= ₹18000

» Income of 2nd person=7x= ₹14000

━━━━━━━━━━━━━━━━━━━━━━━━━