Let's Ram's age be x at the end of 2002.
And Grandpa's age be 2x.
Ram's birth year=2002-x
Grandpa's birth year=2002-2x
Now,
(2002-x)+(2002-2x)=3854......(sum of born years)
=> x=50
So Ram was born in year 1952
And Ram's age at the end of 2003 would be 51 years
Ans 51 years.