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Question

(C) Let the third number be $x$.Then,the second number $= 2x$.The first number $= 2 	imes (2x) = 4x$.The reciprocals of the numbers are $\frac{1}{4x}

Vedclass · Accepted Answer

$24, 12, 6$

Vedclass · Answer

(C) Let the third number be $x$.Then,the second number $= 2x$.The first number $= 2 	imes (2x) = 4x$.The reciprocals of the numbers are $\frac{1}{4x}, \frac{1}{2x}, 	ext{ and } \frac{1}{x}$.The average of these reciprocals is given by $\frac{1}{3} \left( \frac{1}{4x} + \frac{1}{2x} + \frac{1}{x} ight) = \frac{7}{72}$.Simplifying the expression inside the parentheses: $\frac{1+2+4}{4x} = \frac{7}{4x}$.So,$\frac{1}{3} 	imes \frac{7}{4x} = \frac{7}{12x} = \frac{7}{72}$.By cross-multiplying,$12x = 72$,which gives $x = 6$.Therefore,the numbers are $4x = 24$,$2x = 12$,and $x = 6$.

Of the three numbers,the first is twice the second and the second is twice the third. The average of the reciprocals of the numbers is $\frac{7}{72}$. The numbers are:

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