Question

A natural number when increase by 12 becomes equal to 160 times of its reciprocal. Find the number.

Answer 1

Answer:

let the required number be x

ATQ, x+12 = 160 (1/x)

x+12 = 160/x

xsquare+12x-160 = 0

xsquare+20x-8x-160 = 0

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

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

x = -20,8

-20 will be rejected as the number is a natural number

therefore x = 8

Answer 2

Answer:

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

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