Question

The ratio of the annual income of A and B is 5 : 4 and the ratio of their expenditures is 11 : 8. If each saves ₹ 4000. Find their annual incomes.

Answer 1

Given:

• Ratio of annual incomes of A and B = 5 : 4
• Ratio of their expenditures = 11 : 8
• Each saves ₹ 4000

Step-wise calculation:

1. Let the annual income of A = 5x and the annual income of B = 4x.

2. Let the annual expenditure of A = 11y and the annual expenditure of B = 8y.

3. Since savings are income minus expenditure, the savings of each = ₹ 4000, so:

For A: 5x – 11y = 4000   ...(i)

For B: 4x – 8y = 4000   ...(ii)

4. Multiply equation (i) by 4 and equation (ii) by 5 to equalize the x terms:

20x – 44y = 16000

20x – 40y = 20000

5. Subtract the second equation from the first:

(20x – 44y) – (20x – 40y) = 16000 – 20000

–44y + 40y = –4000

–4y = –4000

y = 1000

6. Substitute y = 1000 in (ii):

4x – 8(1000) = 4000

4x – 8000 = 4000

4x = 12000

x = 3000

7. Calculate annual incomes:

Income of A = 5x

Income of A = 5 × 3000

Income of A = ₹ 15000

Income of B = 4x

Income of B = 4 × 3000

Income of B = ₹ 12000

The annual income of A is ₹ 15,000 and the annual income of B is ₹ 12,000.