The ratio of incomes of Venkanna and Saidulu is 7 : 5 and ratio of their expenditures is 3 : 2. If each person saves Rs. 3,000, then find the sum of their incomes.

Given:

Ratio of incomes of Venkanna and Saidulu = 7 : 5

Ratio of their expenditures = 3 : 2

Each person saves Rs. 3,000.

Calculation:

Let the incomes of Venkanna and Saidulu be 7x and 5x, respectively.

Let the expenditures of Venkanna and Saidulu be 3y and 2y, respectively.

Forming Equations:

Income - Expenditure = Savings

For Venkanna: 7x - 3y = 3000

For Saidulu: 5x - 2y = 3000

Solving for x and y:

Multiply the first equation by 2 and the second equation by 3:

2(7x - 3y) = 2(3000) → 14x - 6y = 6000

3(5x - 2y) = 3(3000) → 15x - 6y = 9000

Subtract the two equations:

(15x - 6y) - (14x - 6y) = 9000 - 6000

x = 3000

Finding Total Income:

Total income = 7x + 5x = 12x

⇒ 12 × 3000 = 36,000

Final Answer:

The sum of their incomes is Rs. 36,000.