Multiple choice

The ratio of incomes of two persons is 5 : 3 and that of then expenditure is 9 : 5. Find the income of each person if they save Rs. 1300 and Rs. 900 respectively.

  1. Rs. 4000, Rs. 2400

  2. Rs. 3000, Rs 1800

  3. Rs. 5000, Rs. 3000

  4. Rs. 4500, Rs. 2900
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A Correct answer
Explanation

Income ratio 5:3, expenditure 9:5, savings 1300 and 900. (5x - 1300) / (3x - 900) = 9/5. 25x - 6500 = 27x - 8100 => 2x = 1600 => x = 800. Incomes are 5*800=4000 and 3*800=2400.

AI explanation

Let the incomes be 5x and 3x, and the expenditures be 9y and 5y. Using the formula Income - Expenditure = Savings, we establish 5x - 9y = 1300 and 3x - 5y = 900. Solving these simultaneous equations gives x = 800 and y = 300. The respective incomes are 5 multiplied by 800 and 3 multiplied by 800, which are Rs. 4000 and Rs. 2400.

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