Let x be a natural number.
According to the question, when 12 is added to a natural number.
It becomes 160 times its reciprocal
x + 12 = 160 × 1/x
⇒ x2 + 12x = 160
⇒ x2 + 12x – 160 = 0
⇒ x2 + (20 – 8) x – 160 = 0
⇒ x2 + 20x – 8x – 160 = 0
⇒ x (x + 20) – 8 (x + 20) = 0
⇒ (x + 20) (x – 8) = 0
if x + 20 = 0, then x = -20
or x – 8 = 0, then x = 8
x is a natural number,
so it cannot be negative
x = 8
Hence, number is 8.