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 their
monthly incomes.
Solution
I et us denote the incomes of the two person by 9x and * 7x and their why this is possible ​

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 manages to save 2000 per month.

To find :-

Find their monthly incomes.

Solution :-

• The ratio of incomes of two persons = 9 : 7
• The ratio of their expenditures = 4 : 3
• Each of them manages to save = 2000

Let the income of two persons be 9x and 7x

• Expenditure of two persons be 4y and 3y

According to the given condition

• 9x - 4y = 2000 ----(i)

• 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

→ - x = - 2000

→ x = 2000

Put the value of x in equation (ii)

→ 7x - 3y = 2000

→ 7 × 2000 - 3y = 2000

→ 14000 - 3y = 2000

→ 14000 - 2000 = 3y

→ 12000 = 3y

→ y = 12000/3

→ y = 4000

Hence,

• Monthly income of two persons = 9x and 7x = Rs.18000 and Rs.14000

• Expenditure of two persons = 4y and 3y = Rs.16000 and Rs.12000

Answer 2

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 their monthly incomes.