Question

A natural number when increased by 12 equals 160 times its reciprocle 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