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 ₹).

Let, the monthly income of A = 11x The monthly income of B = 13x The monthly expenditures of A = 9y The monthly expenditures of B = 11y So, 11x - 9y = 4000 .....(1) 13x - 11y = 4000 .....(2) (1) × 11 - (2) × 9 gives, 121x - 99y - 117x + 99y = 44000 - 36000 ⇒ 4x = 8000 ⇒ x = 8000/4 = 2000 ∴ A's income = 11 × 2000 = Rs. 22000 ∴ B's income = 13 × 2000 = Rs. 26000 The difference of income = 26000 - 22000 = Rs. 4000 Alternate method The difference = 2 ratio = Rs. 4000 Their income difference = 13 - 11 = 2 ratio ∴ Income difference = Rs. 4000 ∴ The difference between A and B's incomes (in Rs.) is Rs. 4000