Question

A number when increased by 12 is equal to 160 times of its reciprocal find the number.

Answer 1

$let \: the \: number \: be \: x$

$then \: its \: reciprocal \: will \: be \: \frac{1}{x}$
A/Q :-
$= x + 12 = 160( \frac{1}{x} ) \\ \\ = x + 12 = \frac{160}{x} \\ \\ = x(x + 12) = 160 \\ \\ = {x}^{2} + 12x = 160 \\ \\ = {x}^{2} + 12x - 160 = 0 \\ \\ = {x}^{2} + (20 - 8)x - 160 = 0 \\ \\ = {x}^{2} + 20x - 8x - 160 = 0 \\ \\ = x(x + 20) - 8(x + 20) = 0 \\ \\ = (x + 20)(x - 8) = 0 \\ \\ therefore \\ x = (- 20) \: or \: 8$

Answer 2

Answer:

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

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