Question

A man in 1900s realised that in 1980 his age was the square root of the year of his birth. What is his birth year ?

(a) 1929 

(b) 1949 

(c) 1936 

(d) 1946

Answer 1

(c) 1936

Let the year of his birth be x. 

∴ His age (in years ) = 1980 – x

Given, 1980 - x = \(\sqrt{x}\)

⇒ x + \(\sqrt{x}\) - 1980 = 0

⇒ y² + y - 1980 = 0            (Let \(\sqrt{x}\) = y)

⇒ (y + 45)(y - 44) = 0 ⇒ y = -45, 44

Rejecting –ve value, y = 44

⇒ \(\sqrt{x}\) = 44 ⇒ x = (44)² = 1936.