Question

The incomes of A and B are in the ratio 9:4 and their expenditures are in the ratio 7:3. If A saves 30% of his income, then the ratio of their savings is:

• A. 63 : 32
• B. 69 : 35
• C. 9 : 5
• D. 36 : 23

Hint:

To find the ratio of savings, first express savings as the difference between income and expenditure, then use the given percentages to form equations.

Answer 1

The Correct Option is A

Let the income of A be \( 9x \) and the income of B be \( 4x \). Let the expenditure of A be \( 7y \) and the expenditure of B be \( 3y \). We know that A saves 30% of his income, so the savings of A is: \[ \text{Savings of A} = 30% \times 9x = 0.30 \times 9x = 2.7x. \] The savings of A is also given by: \[ \text{Savings of A} = \text{Income of A} - \text{Expenditure of A} = 9x - 7y. \] Thus, \[ 2.7x = 9x - 7y \quad \Rightarrow \quad 7y = 6.3x \quad \Rightarrow \quad y = 0.9x. \] Now, the savings of B is: \[ \text{Savings of B} = 4x - 3y = 4x - 3(0.9x) = 4x - 2.7x = 1.3x. \] Thus, the ratio of the savings of A and B is: \[ \frac{\text{Savings of A}}{\text{Savings of B}} = \frac{2.7x}{1.3x} = \frac{2.7}{1.3} = \frac{27}{13} = 63 : 32. \] Thus, the ratio of their savings is 63 : 32, which corresponds to option (1).