Rohan was born in 19th century, he will be x year old in x^2 year. Find in which year was he born?

Question

If at the end of year 2002, Ram was half old as his grandpa. Sum of the years in which they were born is 3854. What would be the age of Ram at the end of year 2003.

Answer 1

There are 2 answers:
1. 1806
at his 43 years age the year is 1849
so, his age = 43 in year 43^2=1849
2. 1892
at his 44 years age the year is 1936
so,his age = 44 in year 44^2=1936
so, if rohan is born and died in 19th century then,he was born in 1806
but the question is asked Rohan was born in 19th century, he will be x year old in x^2 year. Find in which year was he born?
so, 1806 or 1892