Of the three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the numbers is $\frac{7}{72} .$ The numbers are:
A. 36, 18, 9 B. 24, 12, 6 C. 20, 10, 5 D. 16, 8, 4

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Answer-B Solution-

Solution(By Apex Team)

$\begin{array}{l}\text{Let three numbers be x y and z.}\\ \text{Given, }\\ x=2y\\ \Rightarrow x=4z\\ \Rightarrow y=2z\\ \Rightarrow z=z\\ \text{The average of reciprocal numbers is}\ \Large\frac{7}{72}\\ \Large\frac{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}{3}=\frac{7}{72}\\ \Rightarrow\Large\frac{yz+xz+xy}{3xyz}=\frac{7}{72}\\ \Rightarrow\left(14z^224z^3\right)=\frac{7}{72}\\ \Rightarrow504=84z\\ z=6\\ \text{ So, }x=4z=4\times6=24,\\ \Rightarrow y=2z=2\times6=12\\ \text{ Thus the numbers are }24,12,6\end{array}$

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