Question

A naturaL number increase by 12 equals 160 times it's reciprocal. Find the number

Answer 1

Answer: 8

let the natural number be x.

as per the question,

x + 12 = x ×$\frac{1}{x}$

=> $x^{2} + 12x -160 = 0$

=> $x^{2} + 20x - 8x -160 = 0$

=> $x(x+20) -8(x+20)$

=>$(x+20)(x-8)=0$

=> x = 8   (neglecting the negative one)

proof

8 +12 = 20

160× $\frac{1}{8}$ = 20

Answer 2

Answer:

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

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