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 6/7 of the expenditure of B, then the ratio of the savings of A and B is :

Correct option is C

​$$\textbf{Given:} \\\text{Ratio of incomes of A and B} = 3 : 5 \\\text{Ratio of expenditures of A and B} = 2 : 3 \\\text{Income of A} = \frac{6}{7} \text{ of expenditure of B} \\\textbf{Concept Used:} \\\text{Income, expenditure and savings} \\\textbf{Formula Used:} \\\text{Savings} = \text{Income} - \text{Expenditure} \\\textbf{Solution:} \\\text{Let incomes of A and B be } 3x \text{ and } 5x \\\text{Let expenditures of A and B be } 2y \text{ and } 3y \\\text{Given } 3x = \frac{6}{7} \times 3y \\3x = \frac{18y}{7} \\x = \frac{6y}{7} \\\text{Income of A} = 3x = 3 \times \frac{6y}{7} = \frac{18y}{7} \\\text{Income of B} = 5x = 5 \times \frac{6y}{7} = \frac{30y}{7} \\\text{Expenditure of A} = 2y \\\text{Expenditure of B} = 3y \\\text{Savings of A} = \frac{18y}{7} - 2y \\= \frac{18y - 14y}{7} \\= \frac{4y}{7} \\\text{Savings of B} = \frac{30y}{7} - 3y \\= \frac{30y - 21y}{7} \\= \frac{9y}{7} \\\text{Ratio of savings of A and B} \\= \frac{4y}{7} : \frac{9y}{7} \\= 4 : 9 \\\textbf{Final Answer:} \\4 : 9$$​​