Question

If the arithmetic mean and geometric mean of two numbers are 36 and 30 respectively, then their harmonic mean is:

• A. 100
• B. 75
• C. 50
• D. 25

Hint:

Exam Tip:
For two numbers: \[ G^2 = A \times H \] where \(A\) is arithmetic mean, \(G\) is geometric mean, and \(H\) is harmonic mean.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For two numbers, the relationship between arithmetic mean (A), geometric mean (G), and harmonic mean (H) is: \[ G^2 = A \times H \]

Step 2: Key Formula or Approach:
Given: \(A = 36\), \(G = 30\).
Using the relationship: \[ 30^2 = 36 \times H \Rightarrow 900 = 36H \Rightarrow H = \frac{900}{36} = 25 \]

Step 3: Detailed Explanation:
The harmonic mean is 25.
This relationship holds for any set of positive numbers.

Step 4: Final Answer:
Therefore, option (D) is correct.