Question : The ratio of the monthly incomes of X and Y is 5 : 4 and that of their monthly expenditures is 9 : 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?
Option 1: 9 : 8
Option 2: 6 : 7
Option 3: 8 : 9
Option 4: 7 : 6
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Correct Answer: 9 : 8
Solution : The ratio of the monthly income of X and Y = 5 : 4 The ratio of monthly expenditures of X and Y = 9 : 7 Let the income ratio of X and Y be 5a and 4a. Let the expenditure ratio of X and Y be 9b and 7b. Here, 4a = 9b ⇒ $\frac{\text{a}}{\text{b}}$ = $\frac{9}{4}$ So, Savings of X = 5a – 9b and Savings of Y = 4a - 7b Required ratio $=\frac{(5\text{a} - 9\text{b})}{(4\text{a} - 7\text{b})}$ $=\frac{(45 - 36)}{(36 - 28)}$ $=\frac{9}{8}$ Hence, the correct answer is 9 : 8.
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