Of three numbers, first is twice second and second is twice third. average of reciprocal of numbers

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4.Average

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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

$16,\,8,\,4$

B

$20,\,10,\,5$

C

$24,\,12,\,6$

D

$36,\,18,\,9$

Solution

Let the third number be $x$

Second number $=2 \times x=2 x$

First number $=2 \times 2 x=4 x$

Average of reciprocal of numbers $=\frac{1}{3}\left(\frac{1}{x}+\frac{1}{2 x}+\frac{1}{4 x}\right)$

$=\frac{1}{3 x}\left(\frac{4+2+1}{4}\right)=\frac{7}{12 x}=\frac{7}{72}$

$x=6$

Numbers are $6,12,24$

Standard 13

Quantitative Aptitude

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