Multiple choice

Two partners divide a profit of $6,000 between themselves such that the difference between the two amounts is 2/3 of their average. What is the ratio of the larger amount to the smaller amount?

  1. 2 : 1

  2. 5 : 1

  3. 4 : 3

  4. 3 : 2

  5. 3 : 1
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A Correct answer
Explanation

Let the amounts be x and y with x > y. The average is (x+y)/2. The difference x-y = (2/3) * ((x+y)/2) = (x+y)/3. Solving 3x - 3y = x + y gives 2x = 4y, or x/y = 2/1.

AI explanation

Let the two amounts of the profit be x and y, where x is the larger amount; their sum is 6000, making their average 3000. The problem states the difference between the amounts is two-thirds of this average, so x - y equals two-thirds of 3000, which is 2000. Solving the system of equations x + y = 6000 and x - y = 2000 gives the larger amount as 4000 and the smaller amount as 2000. The ratio of the larger amount to the smaller amount is therefore 2 to 1.

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