Question

A person was asked to state his age in years. His reply was “Take my age three years hence multiply it by 3 and then subtract three times my age 3 years ago and you will know how old I am.” What was the age of the person?
A). 18 years
B). 20 years
C). 24 years
D). 32 years

Answer 1

Hint: Start by assuming the present age as some variable and try to form relations as per the statement given in the question. Solve the relationships formed and find out the value of the variable assumed, ignore negative value if found as age can never be negative.

Complete step by step solution:
Let us take the present age of the person to be ‘x’ years.
Now, let us form the required relation of ages.
The age of the person 3 years from now will be=$x+3$years
The age of the person 3 years ago was =$x-3$years
Now, according to the statement given in the question, we have
$3(x+3)-3(x-3)=x$
Solving this, we get
$$\begin{gathered} 3x+9-3x+9=x \\ \Rightarrow x=18 \end{gathered}$$

Therefore, the present age of the person is 18 years. So, option A is the correct answer.

Note: Such similar problems can be solved by following the approach of part by part work, read a statement, and then form its equation or relation and repeat the same for the next statement. Attention is required while solving such questions as they can have quadratic equations, needed to be solved by either splitting middle term or discriminant rule and any negative values are to be neglected as age can never be negative.