Multiple choice

The ratio of incomes of Alexander and Ibrahim is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs. 5200 and Rs. 3600, then their incomes are

  1. Rs. 16000 and Rs. 9600

  2. Rs. 12000 and Rs. 7200

  3. Rs. 20000 and Rs. 12000

  4. Rs. 18000 and Rs. 10800

  5. Rs. 22000 and Rs. 14000
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A Correct answer
Explanation

Let incomes be 5x and 3x, expenditures 9y and 5y. 5x - 9y = 5200 and 3x - 5y = 3600. Solving this system: multiply first by 3 and second by 5: 15x - 27y = 15600 and 15x - 25y = 18000. Subtracting gives 2y = 2400, so y = 1200. Then 3x - 6000 = 3600, 3x = 9600, x = 3200. Incomes are 5(3200)=16000 and 3(3200)=9600.

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 = 5200 and 3x - 5y = 3600. Solving these simultaneous equations gives x = 3200 and y = 1200. The respective incomes are 5 multiplied by 3200 and 3 multiplied by 3200, which are Rs. 16000 and Rs. 9600.

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