Question

9 years hence, a girl will be 3 times as old as she was 9 years ago. How old is she now?

Answer 1

Hint: Type of question is based on the age problem, So we will first assume the age of girl by some variable, and go according to question, and finally make relation according to given condition in question which will give us linear equation in one variable which on further solving give the answer.

Complete step-by-step solution:
Moving ahead with the question in a stepwise manner;
Let the age of the girl be x years now.
Since ‘hence’ means after so according to question 9 year hence girl will be$=x+9$
And girl age before 9 years from now will be$=x-9$
So according to the question, after 9 years the girl will be three times her age. She will be 9 years from now. So after 9 years we will have three times the value that we had 9 years before from now. So if we multiply the 9 year before age by three then we will get the exact age which a girl will have after 9 years from now. So we will get;
Girl age after 9 years is equal to 3 times of girl’s age before 9 years, so we will have;
$x+9=3(x-9)$
Solving it further we will get;
$\begin{align}
  & x+9=3x-27 \\
 &\Rightarrow 2x=36 \\
 &\Rightarrow x=18 \\
\end{align}$
So we got the value of ‘x’ i.e. 18, which is the present age of a girl.
Hence the answer is 18, i.e. the present age of a girl is 18 years.

Note: To get the final answer our aim is to make a relation between the given condition, as we did by multiplying 3 with the girl’s age before 9 years from now in order to equate it with girl’s age after 9 years. Here we had only one variable so there we needed only one equation and found the answer.