Question

A man born in the first half of the nineteenth century was x years old in the year $x^{2}$. He was born in :
A. 1849
B. 1825
C. 1812
D. 1836
E. 1806

Answer 1

Hint: Start by taking the year span in which he must have been born , and then take his age as x and try to find the year in consideration as $x^{2}$. Hit and Trial is to be used here by taking random age falling under the year span in consideration, the value which satisfies both the conditions will be his age . Subtract this age from the year in order to find out his year of birth.

Complete step by step answer:
It is given that the man was born in the first half of the nineteenth century, which means he was born somewhere between 1800 – 1850.
And according to the statement his age was x years in the year $x^{2}$ , Which means the square of his age would give us the year in which his age was taken into count or vice-versa.
So , Let us start by checking the numbers in between 1800 – 1850 which will be a square of any natural number.
If we take his age as 40 then square of his age = 1600 < 1800. Therefore, we need to increase the age.
Let’s take age= 41 and square of his age = 1681 < 1800.
Now, Let’s take age= 43 , then it’s square = 1849 > 1800 and less than 1850.
So, The person’s age is 43 in the year 1849.
Therefore, He must be born in the year 1849 – 43 = 1806.

So, the correct answer is “Option E”.

Note: Such questions at first glance might look confusing. The best way to solve such questions is to break down all the statements or information into smaller parts, and then continue with the set procedure.