Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. The ratio of incomes of two persons is 5:3 and that of their expenditures is 9:5. If they save Rs 2600 and Rs 1800 respectively, their incomes are

  1. 9000, 5400

  2. 10000, 6000

  3. 6000, 3600

  4. 8000, 4800

  5. 2600, 1800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 5x and 3x. Expenditures are 9y and 5y. 5x - 9y = 2600 and 3x - 5y = 1800. Solving this system: multiply first by 5 and second by 9: 25x - 45y = 13000 and 27x - 45y = 16200. Subtracting gives 2x = 3200, x = 1600. Incomes are 5*1600 = 8000 and 3*1600 = 4800.

AI explanation

Let the incomes of the two persons be 5x and 3x, and their expenditures be 9y and 5y respectively. Since their savings are Rs. 2600 and Rs. 1800, we set up the equations 5x minus 9y = 2600 and 3x minus 5y = 1800. Multiplying the first equation by 5 and the second by 9 gives 25x minus 45y = 13000 and 27x minus 45y = 16200. Subtracting the first modified equation from the second yields 2x = 3200, meaning x = 1600. The incomes of the two persons are 5x and 3x, which equal Rs. 8000 and Rs. 4800 respectively.

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