A natural number, when increased by 12, is the same as 160 times it is reciprocal. Find out the number.

Solution

Assume the natural number = x
If the number increased by 12 = x + 12
Then,
Reciprocal of the number = 1/x
As per the question, we get,
x + 12 = 160 times of reciprocal for 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 and x = 8
Natural numbers can’t be negative.
Hence,
The required number = x = 8