Question

The ratio of the annual income of A and B is 6 : 5 and the ratio of their expenditures is 5 : 4. If each saves ₹ 10000, find their annual incomes.

Answer 1

Given:

• Ratio of annual incomes of A and B = 6 : 5
• Ratio of their expenditures = 5 : 4
• Each saves ₹ 10,000

Step-wise calculation:

1. Let the annual income of A = 6x and the annual income of B = 5x.

2. Let the annual expenditure of A = 5y and the annual expenditure of B = 4y.

3. Since savings = income – expenditure, we have:

For A: 6x – 5y = 10,000

For B: 5x – 4y = 10,000

4. Multiply the first equation by 4 and the second by 5 to make the y terms comparable:

(6x – 5y) × 4 → 24x – 20y = 40,000

(5x – 4y) × 5 → 25x – 20y = 50,000

5. Subtract the first new equation from the second:

(25x – 20y) – (24x – 20y) = 50,000 – 40,000

x = 10,000

6. Put x = 10,000 into one of the earlier equations:

6(10,000) – 5y = 10,000

60,000 – 5y = 10,000

5y = 60,000 – 10,000

5y = 50,000

y = 10,000

7. Calculate annual incomes:

Income of A = 6x

Income of A = 6 × 10,000

Income of A = ₹ 60,000

Income of B = 5x

Income of B = 5 × 10,000

Income of B = ₹ 50,000

The annual income of A is ₹ 60,000 and the annual income of B is ₹ 50,000.