Question 142

The sum of two numbers is 15 and their gemetric mean is 20% lower than their arithmetic mean. Find the numbers.

Solution

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Arithmetic mean = Sum/2 = 15/2.
Geometric mean = 0.8 * Arithmetic mean = 0.8 * 15/2 = 6.
Product of the 2 numbers will be square of Geometric mean = 36.
Let us assume the numbers to be x and y. 
x + y = 15 and xy = 36. Substituting value of x as 15 - y, we get:
y(15 - y) = 36 ==> $$y^2-15y\ +\ 36\ =\ 0$$.
y = 3 or 12.
So, the two numbers are 12 and 3.

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