Question

At the end of the year 2002, Ram was half as 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: First, we will assume the birth year of Ram and grandpa are some random variable say x and y respectively. Now, we can write that at the end of 2002, their ages will be 2002-x and 2002-y respectively. Then according to the given conditions, we will form a pair of linear equations. Then by substituting values, we will get a value of x. At the end we will subtract it from year 2003 to get the required answer.

Complete step-by-step answer:
Here, we will assume the age of Ram at the end of year 2002 as x. Now, it is told that Ram was half than his grandpa. So, we write that the age of grandpa is twice that of Ram. So, the age of grandpa is $\dfrac{y}{2}$ . We can write it as
$2002-x=\dfrac{2002-y}{2}$
On further solving, we can write it as
$4004-2x=2002-y$
Taking all the terms on RHS side and on solving, we get
$2x-y-2002=0$ ………………………….(1)
Now, it is given that the sum of the years in which they are born is 3854. So, we assume that the birth year of Ram is x and that of his grandpa is y. So, in mathematical form we can write it as
$x+y=3854$ ………………………..(2)
Now, we will make y as subject variable from equation (1). We will get as
$y=2x-2002$
Substituting this value in equation (2), we will get as
$x+2x-2002=3854$
On further solving, we will get as
$3x=3854+2002=5856$
On dividing equation 3 on both sides, we will get
$x=\dfrac{5856}{3}=1952$
Thus, the birth year of Ram is 1952.
So, the age of Ram at the end of year 2003 is $2003-1952=51$ years.
Thus, the age of Ram is 51 years.
Option (c) is the correct answer.

Note: This question is a little tricky one because here, we have to find the age of Ram by using year. So, we must understand that ages are represented in the form of 2002. There are chances of calculation mistakes here, so do not make it and understand the question properly.