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 2003 is ____.
(a)50 years
(b)35 years
(c)51 years
(d)36 years

Answer 1

Hint: In the above question, we will just assume the year of both Ram and his grandpa to be variables and then by using the given condition we will form a pair of linear equations in two variables. After solving the equations we will get the birth year of Ram and his grandpa.

Complete step-by-step answer:

Let, the year in which Ram and his grandpa were born be x and y respectively.

Then, according to the question we have been given, at the end of 2002, Ram was half old as his grandpa.

\[\Rightarrow 2002-x=\dfrac{\left( 2002-y \right)}{2}\]

On further solving the equation we get,

\[2x-y=2002-(1)\]

Also, we have been given that the sum of the years in which they were born is 3854.

\[\Rightarrow x+y=3854-(2)\]

Now adding equation (1) and (2), we get

\[\begin{align}

  & 3x-y+y=2002+3854 \\

 & 3x=5856 \\

 & x=\dfrac{5856}{3} \\

 & x=1952 \\

\end{align}\]

So, the year in which Ram was born in 1952.

Thus, in 2003, Ram’s age would be, 2003 – 1952 = 51 years.

Therefore the correct option is (c).


Note: Just be careful while solving the equations as there is a chance that you might make a mistake and you will get the incorrect answer. This question is a special case where we have to solve using the year given. So, we must not skip this question, but must understand that the ages can be represented in terms of the year 2002 as well.