Multiple choice

Incomes of A and B are in the ratio 3 : 4. The expenditures are in the ratio 4 : 5. Find the ratio of the savings if B saves one - third of his income ?

  1. 13 : 21

  2. 13 : 20

  3. 14 : 23

  4. 12 : 19

  5. None
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B Correct answer
Explanation

Income ratio 3x:4x. Expenditure ratio 4y:5y. Savings = Income - Expenditure. B saves 1/3 of income: 4x - 5y = (1/3)*4x => 12x - 15y = 4x => 8x = 15y => y = 8x/15. Savings A = 3x - 4(8x/15) = 3x - 32x/15 = 13x/15. Savings B = 4x/3 = 20x/15. Ratio 13:20.

AI explanation

Let the incomes of A and B be 3x and 4x, and their expenditures be 4y and 5y. Since B saves one-third of his income, B's savings equal 4x divided by 3, which gives 4x = 12x - 15y, meaning 15y = 8x and y = 8x divided by 15. A's savings are 3x minus 4y, which substitutes to 3x minus 32x divided by 15, resulting in 13x divided by 15. The ratio of A's savings to B's savings is (13x divided by 15) divided by (4x divided by 3), giving 13 : 20.

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