Question

After \[18\] years, Swarnim will be \[4\] times as old as he is now. His present age is ___________.

Answer 1

Hint: When we are required to find an unknown value, always provide a variable for that value say ‘$a$’. We use the concept of linear equations for getting the ‘present age’, since we have only one unknown value. Also we are given a relation from the statement so we can create a linear equation from that given relation.

Complete step by step solution:
Let us start by understanding the concept behind the question.
So we are given a relation where a Swarnim’s age in the future is said to be equal to a multiple of his present age.
The unknown value that we need to compute is Swarnim’s present age so let that be ‘$a$’.
Now we need to translate the statement given in the question into its equivalent linear equation. For this we use the relation of each value given with the present age that we have considered to be ‘$a$’.
The linear equation in words would be:
Swarnim’s age \[18\] years later is Swarnim’s present age times \[4\].
The word ‘is’ in the statement shows us the placement for the ‘equal to’ sign in the linear equation. Here we need to take the portion of the statement before ‘is’ as the left hand side operation to the ‘equal to’ sign and the portion after ‘is’ is on the right side of ‘equal to’ sign.
Operation on the left side: Swarnim’s age \[18\] years later (it has to be \[18\] more than the present age) $ \to 18 + a$
Operation on the right side: Swarnim’s present age times \[4\] (present age multiplied by \[4\]) $ \to 4 \times a$
Therefore the linear equation is a combination of the operations on the left and right sides:
$ \Rightarrow 18 + a = 4 \times a$
Putting all the variables on one side for easy simplification;
$ \Rightarrow 18 = (4 \times a) - (1 \times a)$
Simplifying further;
$ \Rightarrow 18 = 3 \times a$
 Solving the equation to get;
$ \Rightarrow \dfrac{{18}}{3} = a$
$ \Rightarrow a = 6$
So the unknown value is $6$.

Therefore, Swarnim’s present age is $6$ years.

Note:
Most times the questions that involve finding a person’s age can be done similarly using linear equations. Keep in mind that the given statement must be read carefully in order to translate it into the correct linear equation. We must also use our common sense to verify the answer, for example when they give a statement involving a person’s age in the past and future, we know that the age has to increase in the future.