Question

number when increased by 12 equals 160 times its reciprocal find the number

Answer 1

$\huge\boxed{\texttt{\fcolorbox{red}{aqua}{Hey Mate!!!}}}$

Let the number is x

It's reciprocal is 1/x

ATQ
$x + 12 = 160 \times \frac{1}{x} \\ x(x + 12) = 160 \\ {x}^{2} + 12x - 160 = 0 \\ {x}^{2} + 20x - 8x - 160 = 0 \\ x(x + 20) - 8(x + 20) = 0 \\ (x + 20)(x - 8) = 0 \\ x = 8 \: \: and \: - 20 \\ \\ since \: number \: is \: not \: negative \: hence \\ x = 8$

Therefore the number is 8

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Answer 2

Answer:

Let the Number be n and, reciprocal be 1 /n.

$\underline{\bigstar\:\textsf{According to the Question Now :}}\\\\\implies\tt n + 12 = 160 \times \dfrac{1}{n} \\\\\\\implies\tt n + 12 = \dfrac{160}{n}\\\\\\\implies\tt n(n + 12) = 160\\\\\\\implies\tt {n}^{2} + 12n = 160\\\\\\\implies\tt {n}^{2} + 12n - 160 = 0\\\\\\\implies\tt {n}^{2} + (20 - 8)n - 160 = 0\\\\\\\implies\tt {n}^{2} + 20n - 8n - 160 = 0\\\\\\\implies\tt n(n + 20) - 8(n + 20) = 0\\\\\\\implies\tt (n - 8)(n + 20) = 0\\\\\\\implies\tt \green{n = 8} \quad or \quad \red{n = - 20} \\\\\\ \therefore \underline{\textsf{Hence, Natural Number will be \textbf{8.}}}$