The ratio of the incomes of A and B is 3 : 5 and the ratio of their expenditures is 2 : 3. If the income of A is equal to \(\frac{6}{7}\) of the expenditure of B, then the ratio of the savings of A and B is :

Given:

Ratio of incomes of A and B = 3 : 5

Ratio of expenditures of A and B = 2 : 3

Income of A is equal to 6/7 of the expenditure of B.

Calculation:

Let the income of A be 3x and the income of B be 5x.

Let the expenditure of A be 2y and the expenditure of B be 3y.

From the third condition, "Income of A is equal to 6/7 of the expenditure of B":

Income of A = (6/7) × Expenditure of B

3x = (6/7) × 3y

3x = 18y / 7

x = 6y / 7

Income of A = 3x = 3 × (6y/7) = 18y/7

Income of B = 5x = 5 × (6y/7) = 30y/7

Expenditure of A = 2y

Expenditure of B = 3y

Savings of A = Income of A - Expenditure of A

= (18y/7) - 2y

= (18y - 14y) / 7

= 4y/7

Savings of B = Income of B - Expenditure of B

= (30y/7) - 3y

= (30y - 21y) / 7

= 9y/7

Ratio of Savings (A : B) = (4y/7) : (9y/7)

= 4y : 9y = 4 : 9

∴ The correct answer is option 4.