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The sum of a number and its reciprocal is $2 \frac{1}{30}$ . Find the number.

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\frac{5}{4}

\frac{4}{5}

\frac{5}{6}, \frac{6}{5}

\frac{5}{3}, \frac{5}{4}

\frac{2}{6}, \frac{6}{5}

answer is B.

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Detailed Solution

Suppose the number= x.
Reciprocal will =

\frac{1}{x}

.
According to the question,

x + \frac{1}{x} = 2 \frac{1}{30}

\Rightarrow \frac{x^{2} + 1}{x} = \frac{61}{30}

\Rightarrow 30 x^{2} + 30 = 61 x

\Rightarrow 30 x^{2} - 61 x + 30 = 0

\Rightarrow 30 x^{2} - 36 x - 25 x + 30 = 0

\Rightarrow 6 x (5 x - 6) - 5 (5 x - 6) = 0

\Rightarrow (6 x - 5) (5 x - 6) = 0

x = \frac{5}{6}

x = \frac{6}{5}

Hence, the required number are

\frac{5}{6}

and

\frac{6}{5}

.
Option 2 is correct.

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