The ratio of the 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₹)

4,000

                       A   :   B

Income           11   :  13

Expenditure      9   :  11

Savings = -   4000   -4000       (Income - Expenditure)

$\frac{11R\;-\;4000}{13R\;-\;4000} = \frac{9}{11}$

Using cross - multiplication, 

121R - 117R = (9 x -4000) - (11 x -4000)

          4R     =  2 x 4000  ⇒     R = 2000

Difference in the income of A and B = 2R = 2 x 2000 = 4000