The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20\%, then what is the difference between the two numbers?

Explanation

a+b=40 \implies \text{AM} = 20. \text{GM} = 20 - 20\% \text{ of } 20 = 16. Since \text{GM} = \sqrt{ab} = 16, ab=256. Using (a-b)^2 = (a+b)^2 - 4ab = 1600 - 1024 = 576, so a-b = 24.

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