If arithmetic mean of two items is 5 and G.M is 4, find their H.M�

Answer 1

To find the Harmonic Mean (H.M.) of two items when their Arithmetic Mean (A.M.) is given as 5 and their Geometric Mean (G.M.) is given as 4, we can use the relationship between these means.

1. The arithmetic mean \( A \) is given by: \[ A = \frac{x + y}{2} = 5 \] Therefore, \[ x + y = 10 \]

2. The geometric mean \( G \) is given by: \[ G = \sqrt{xy} = 4 \] Therefore, \[ xy = 16 \]

Now, we need to find the Harmonic Mean (H.M.), which is given by the formula: \[ H.M. = \frac{2xy}{x+y} \]

3. Substitute \( x + y \) and \( xy \) into the H.M. formula: \[ H.M. = \frac{2 \cdot 16}{10} = \frac{32}{10} = 3.2 \]

Thus, the Harmonic Mean of the two items is \( 3.2 \).