The ratio of the monthly incomes of A and B is 11 : 13 and the ratio of their expenditures is 9 : 11. If both of them manage to save ₹4,000 per month, then find the difference in their incomes (in ₹).

The correct answer is 4,000.

Step-by-Step Explanation:

Let the monthly incomes of A and B be 11x and 13x, respectively, where x is a common multiplier.
Similarly, let the monthly expenditures of A and B be 9y and 11y, respectively, where y is a common multiplier.

We know that:
Income - Expenditure = Saving

Since both A and B manage to save ₹4,000 per month, we can set up the following two linear equations:
For A: 11x - 9y = 4000 (Equation 1)
For B: 13x - 11y = 4000 (Equation 2)

Alternatively, we can observe the difference between the ratio terms.
For A, the income ratio term is 11 and the expenditure ratio term is 9. The difference is:
$11-9=2$ units.
For B, the income ratio term is 13 and the expenditure ratio term is 11. The difference is:
$13-11=2$ units.

Since the difference in ratio units is the same for both A and B (which is 2 units), and their savings are also the same (₹4,000), we can directly equate these 2 units to the savings:
$2\text{units}=4000$
$1\text{unit}=2000$

The question asks for the difference in their incomes.
The difference in their income ratio terms is:
$13-11=2$ units.

Since 2 units correspond to ₹4,000, the difference in their incomes is:
$2\times 2000=4000$

Thus, the difference in their monthly incomes is ₹4,000.