Multiple choice

Aryan and Persian are two brothers who work in a multinational company. The ratio of monthly incomes of Aryan and Persian is 3 : 4 and the ratio of their monthly savings is 2 : 3. It is known that Aryan spends two thirds of his income each month. Which of the following can be the ratio of their monthly expenditures?

  1. 3 : 5

  2. 4 : 5

  3. 5 : 6

  4. 9 : 10
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B Correct answer
Explanation

Let incomes be 3k and 4k, and savings be 2s and 3s. Aryan's expenditure is 3k - 2s = (2/3) * 3k = 2k. Thus, 2s = k. Aryan's savings are 2s = k, so Persian's savings are 3s = 1.5k. Persian's expenditure is 4k - 1.5k = 2.5k. The ratio of expenditures is 2k : 2.5k = 4 : 5.

AI explanation

Let Aryan's income be 3x, so his expenditure of two thirds of his income leaves a savings of x. Given the ratio of their savings is 2 : 3, and since Aryan saves x, Persian saves 1.5x. With Persian's income ratio being 4x and his savings being 1.5x, his expenditure is 4x minus 1.5x, which equals 2.5x. Since Aryan's expenditure is 3x minus x, or 2x, the ratio of Aryan's expenditure to Persian's expenditure is 2x to 2.5x, which simplifies to 4 : 5.

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