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?

Let the two numbers be a and b with a + b = 40, so AM = 20. Given GM = AM - 20% of AM = 0.8 × 20 = 16, so ab = 256. The difference is √((a+b)² - 4ab) = √(1600 - 1024) = √576 = 24.