The arithmetic mean of two numbers is 10 and their geometric mean is 8. What are the two numbers?a)15, 5b)12, 8c)16, 4d)18, 2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Problem: Find two numbers whose arithmetic mean is 10 and geometric mean is 8.

Solution:
Let the two numbers be x and y.

Arithmetic Mean: The arithmetic mean of x and y is given by:
(Arithmetic Mean) = (x + y)/2

Given, the arithmetic mean is 10.
Therefore, we get (x + y)/2 = 10
=> x + y = 20

Geometric Mean: The geometric mean of x and y is given by:
(Geometric Mean) = sqrt(x*y)

Given, the geometric mean is 8.
Therefore, we get sqrt(x*y) = 8
=> x*y = 64

Now, we have two equations:
x + y = 20
x*y = 64

Solving the above equations, we get:
x = 16 and y = 4

Therefore, the two numbers are 16 and 4.
Hence, the correct answer is option C.

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