The product of two numbers is 2160 and their HCF is 12. If the sum of the squares of the two numbers is 4896, then what is the mean of the two numbers?

Explanation

Let the numbers be 12a and 12b. Their product 144ab = 2160 \implies ab=15. Sum of squares 144(a^2+b^2) = 4896 \implies a^2+b^2=34. Using (a+b)^2 = a^2+b^2+2ab = 34+30 = 64 \implies a+b=8. The mean is \frac{12a+12b}{2} = 6(a+b) = 48.

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