Question

A natural number when incresed by 12 equal 160 time its recycled. Find the number

Answer 1

Hi,

Let the natural number = c

If the number increased by 12 = x + 12

Reciprocal of the number = 1/x

According to the problem given,

x + 12 = 160 times of reciprocal of x

x + 12 = 160/ 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 + 20 = 0 or x - 8 = 0

x = - 20 or x = 8

But x is a natural number.

Therefore,

Required number = x = 8

I hope this helps you.

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Answer 2

Answer:

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

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