The ratio of the incomes of A and B is 2 : 3 and that of their expenditures is 1 : 2. If 90% of B’s expenditure is equal to the income of A, then what is the ratio of the savings of A and B?

consider incomes of A=2x

consider incomes of B=3x

consider Expenditure of A=y

consider Expenditure of B=2y

In the question given 90% of B's expenditure is equal to the income of A

$$\frac{90}{100}$$×2y=2x

$$\frac{x}{y}$$=$$\frac{9}{10}$$

x=$$\frac{9}{10}$$y

Formula to find savings is

Savings= Income-Expenditure

Given Income=$$\frac{2x}{3x}$$

          Expenditure=$$\frac{y}{2y}$$

Savings=$$\frac{2x-y}{3x-2y}$$

Substitute x value in the above savings formula then we get

Savings=(2×$$\frac{9}{10}$$y-y)÷(3×$$\frac{9}{10}$$y-2y)

Savings=$$\frac{8÷10}{7÷10}$$

Hence savings=8:7