Question

At the end of the year $2002,$ Ram was half old as his grandpa. The sum of the years in which they were born is $3854$. Age of Ram at the end of year $2003$ is _______.

• A. $50$ years
• B. $35$ years
• C. $51$ years
• D. $36$ years

Answer 1

The correct option is C $51$ years

Let us assume that Ram was born in year $y$ and his grandpa was born in year $x$

Given that,

$x+y=\mathrm{3854......}\left(1\right)$

Also, let us assume age of Grandpa to be $2z$ in year $2002$

$\Rightarrow$ Age of Ram in $2002=z$

$\therefore 2002-x=2(2002-y)$

$2y-x=\mathrm{2002......}\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$ we get, $y=1952$ and $x=1902$

Age of Ram at the end of $2003=2003-1952=51$ years