Question

A natural number when increased by 12 equal 160 times it's reciprocal

Answer 1

Answer:

8

Step-by-step explanation:

Writing the question in equation form.

suppose the natural no is x

x+12=160/x

x^2+12x-160=0

solve for x

we get 8 and -20

natural no is 8 hence 8 is answer.

Answer 2

Answer:

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

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