Multiple choice

A, B and C can do a piece of work in 20, 30 and 40 days, respectively. They earn $5,200 for completing the work.Quantity A Difference between A's money and B's money Quantity B Difference between B's money and C's money

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
Explanation

Their work rates are proportional to 1/20, 1/30, and 1/40, or 6:4:3. Their earnings follow this ratio, so the difference between A's and B's earnings is twice the difference between B's and C's earnings.

AI explanation

The ratio of A, B, and C's efficiencies is the inverse of their time ratios, which is 1/20 : 1/30 : 1/40, simplifying to 6 : 4 : 3. Distributing the \$5,200 in this 13-part ratio gives A \$2,400, B $1,600, and C $1,200. Quantity A is 2400 - 1600 = 800, while Quantity B is 1600 - 1200 = 400, making Quantity A greater.

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