Question

A natural number when increased by 12 equals 160 times its reciprocal. 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.

:)

Answer 2

Heya

let the natural numbe be " n "

when it is increased by 12

it will be n +12

and when it will be n+12

it will equal to 160 times of its reciprocal

reciprocal of n would be 1/n

and now According to given condition

n+12 = 160 X 1/n

n+12 = 160/n

n^2 + 12n = 160

solve the quadratic equation by factorization

n^2 + 12n - 160 = 0

n^2 + 20n - 8n - 160 = 0

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

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

n = - 20

or

n = 8

n = -20 is not not possible because value of natural numbers always positive

so the required number n = 8