Two-third of a positive number and frac{25}{2 | vedclass

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(A) Let the positive number be $x$.According to the problem,two-third of the number is equal to $\frac{25}{216}$ of its reciprocal.So,$\frac{2}{3} x =

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(A) Let the positive number be $x$.According to the problem,two-third of the number is equal to $\frac{25}{216}$ of its reciprocal.So,$\frac{2}{3} x = \frac{25}{216} 	imes \frac{1}{x}$.Multiplying both sides by $x$,we get $\frac{2}{3} x^2 = \frac{25}{216}$.Now,$x^2 = \frac{25}{216} 	imes \frac{3}{2}$.$x^2 = \frac{25}{72 	imes 2} = \frac{25}{144}$.Taking the square root of both sides,$x = \sqrt{\frac{25}{144}} = \frac{5}{12}$ (since the number is positive).

Two-third of a positive number and $\frac{25}{216}$ of its reciprocal are equal. The number is

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