AP & GP of a numbers is given find out their HP.
2025
AP & GP of a numbers is given find out their HP.
- A.
GP/AP
- B.
GP^2*AP
- C.
GP^2/AP
- D.
None of these
Attempted by 27 students.
Show answer & explanation
Correct answer: C
Solution:
Let the two numbers be a and b.
Arithmetic mean (AP) = (a + b)/2.
Geometric mean (GP) = √(ab), so GP² = ab.
Harmonic mean (HP) = 2ab/(a + b).
Compute AP × HP = ((a + b)/2) × (2ab/(a + b)) = ab.
Since GP² = ab and AP × HP = ab, we have AP × HP = GP², so HP = GP² / AP.
Therefore the harmonic mean is GP²/AP.