The ratio of monthly incomes of A and B is 7 : 10. The ratio of their expenditures is 2 : 3. If each of A and B saves 1,000 per month, then what will be the monthly income of B ?

To find the monthly income of B, we use the relationship Income - Expenditure = Savings. Let the monthly incomes of A and B be 7x and 10x, and their expenditures be 2y and 3y respectively. Given that each saves 1,000, we form two equations: 7x - 2y = 1,000 and 10x - 3y = 1,000. To solve for x, we multiply the first equation by 3 and the second by 2, resulting in 21x - 6y = 3,000 and 20x - 6y = 2,000. Subtracting the second from the first gives x = 1,000. Since the monthly income of B is represented by 10x, his income is 10 * 1,000 = 10,000. This method follows standard ratio and proportion techniques where finding the value of one 'part' or variable is the primary objective.