Final answer:
The ratio of the expenditures of A and B is 3:5, which can be determined by using the given income and savings ratios, along with the condition that B's income is three times A's savings.
Step-by-step explanation:
Your question refers to finding the ratio of the expenditures of A and B given the ratios of their incomes and savings, and a condition on B's income in relation to A's savings. To solve this problem, let's denote A's income by 3x, B's income by 5x (where x is a common multiplier), A's savings by 2y, and B's savings by 3y. According to the problem's condition, the income of B (5x) is equal to three times the saving of A (3×2y or 6y).
Therefore, we can express B's income in terms of A's savings: 5x = 6y. This allows us to solve for the ratio of x to y, which is necessary to determine expenditures. Expenditure is the difference between income and savings. Thus, the expenditure of A is 3x - 2y and that of B is 5x - 3y.
Using the relationship 5x = 6y, we can express A's expenditure in terms of y (3×6y/5 - 2y) and B's expenditure in the same terms (6y - 3y). Simplifying these expressions, we find that the ratio of A's expenditure to B's expenditure is 9y/5 to 3y, which simplifies to 9:15 or 3:5 when reduced to the simplest form. This is the ratio of the expenditures of A and B.