A natural number, when increased by 12, becomes equal to 160 times its

1.	A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
Answer» 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

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

Answer»

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

n = 8

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

so the required number n = 8