GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 6

A number x is said to be the harmonic mean of y and z if 1/x is the average of 1/y and 1/z. Harmonic mean of 30 and 45 is _____________ .
(A) 37.5
(B) 72
(C) 18
(D) 36


Answer: (D)

Explanation: Let a = 1/y and b = 1/z. The average of a, b is,

= (a+b)/2 = (1/y+1/z)/2 = (y+z)/(2yz) 

The Harmonic mean x is the reciprocal of this average so,

x = (2yz)/(y+z) 

Given,

y = 30, z = 45 

Therefore,

x = (2yz)/(y+z) = (2×30×45)/(30+45) = 36 

Option (D) is correct.

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