Q249 / 270 · NDA 2021 (Phase 2) · Mathematics

If the harmonic mean of 60 and $x$ is 48 , then what is the value of $x$ ?

  • A
    32
  • B
    36
  • Correct answer
    C
    40
  • D
    44

Solution

If the Harmonic mean of 60 and $x$ is 48 , then $\begin{aligned} & \frac{2}{48}=\frac{1}{60}+\frac{1}{x} \\ & \frac{1}{x}=\frac{2}{48}-\frac{1}{60}=\frac{1}{12}\left[\frac{2}{4}-\frac{1}{5}\right] \\ & \frac{1}{x}=\frac{1}{12} \times \frac{10-4}{20}=\frac{6}{12 \times 20} \\ & \therefore x=40 \end{aligned}$

Hence, the correct answer is option: 'C'.

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