Multiple choice

The incomes of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's savings are one-fourth of his income, then the ratio of savings of A, B and C is

  1. 56 : 99 : 69

  2. 99 : 56 : 69

  3. 69 : 56 : 99

  4. 99 : 69 : 56
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A Correct answer
Explanation

Income ratio 7x:9x:12x. A's savings = 1/4 * 7x = 1.75x. A's expenditure = 7x - 1.75x = 5.25x. Ratio of expenditures is 8:9:15. If 8k = 5.25x, then k = 5.25x/8. B's exp = 9k = 5.90625x. C's exp = 15k = 9.84375x. Savings: A=1.75x, B=9x-5.90625x=3.09375x, C=12x-9.84375x=2.15625x. Ratio 1.75 : 3.09375 : 2.15625 simplifies to 56:99:69.

AI explanation

Let the incomes of A, B and C be 7x, 9x and 12x, and their expenditures be 8y, 9y and 15y. Since A's savings are one-fourth of his income, 7x - 8y = 7x/4, which simplifies to 21x = 32y. Multiplying the income and expenditure ratios by 32 and 21 respectively to equate the variables gives incomes of 224, 288 and 384, and expenditures of 168, 189 and 315. The savings are 56, 99 and 69, making the ratio 56:99:69.

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