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

Given

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

Find out

We have to determine the natural number

Solution

Let us assume the natural number to be = ‘n’.

According to the given details, the quadratic equation formed is

n + 12 = 160 times of reciprocal of n

n + 12 = 160/ n

n( n + 12 ) = 160

n2 + 12n – 160 = 0

n2 + 20n – 8n – 160 = 0

n( n + 20) – 8( n + 20)= 0

(n + 20) (n – 8) = 0

n + 20 = 0 or n – 8 = 0

n = – 20 or n = 8

Since, natural numbers cannot be negative.

The required number = n = 8

Answer

The natural number when increased by 12, equals 160 times its reciprocal is 8

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