Question

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

Answer 1

Let the natural number = x

When the number increased by 12 = x + 12

Reciprocal of the number = `1/x`

According to the question, we have,

x + 12 = 160 times of reciprocal of x

x + 12 = `160/x`

x(x + 12) = 160

x² + 12x – 160 = 0

x² + 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

Since, natural numbers cannot be negative.

The required number = x = 8