Question

Five years ago the age of Ankita was thrice the age of Ajita. After ten years Ankita’s age will be twice the age of Ajita. Find the present ages of Ankita and Ajita.

Answer 1

Hint: Suppose the current age of Ankita and Ajita as two different variables. Then, use the given conditions to write two equations. Now, solve the 2 equations to get the values of the variables and eventually get the age of Ankita and Ajita.

Complete step-by-step solution:
Let the present age of Ankita be $ x $ years and the present age of Ajita be $ y $ years. Now, according to the question five years ago Ankita was thrice the age of Ajita.
Therefore, five years ago:
Ankita's age $ = x - 5 $ years
Ajita's age $ = y - 5 $ years
Ankita's age = thrice the Ajita's age
\[
   \Rightarrow x - 5 = {\text{ }}3\left( {y - 5} \right) \\
   \Rightarrow x - 5 = {\text{ }}3y - 15 \\
   \Rightarrow x - 3y + 10 = 0 - - - - - (i) \\
 \]
Now, again as given in the question;
Ankita's age= twice the Ajita's age
So, ten years after,
Ankita's age \[ = x + 10\]
Ajita's age \[ = y + 10\]
Now, the relation between their ages:
\[
   \Rightarrow x + 10 = 2\left( {y + 10} \right) \\
   \Rightarrow x + 10 = 2y + 20 \\
   \Rightarrow x - 2y - 10 = 0 - - - - - (ii) \\
 \]
Now, solve the equation \[\left( i \right){\text{ and }}\left( {ii} \right)\] to get \[x{\text{ and }}y\]
From equation $ (i) $
Value of \[x = {\text{ }}3y - 10 - - - - \left( {iii} \right)\]
Putting value of \[x{\text{ from Eq}}\left( {iii} \right){\text{ in Eq}}\left( {ii} \right),\] we get,
\[
   \Rightarrow 3y - 10 - 2y - 10 = 0 \\
   \Rightarrow y = 20 \\
 \]
Now putting the value of \[y{\text{ in Eq}}\left( {iii} \right)\]
We get,
\[
   \Rightarrow x = 3\left( {20} \right) - 10 \\
   \Rightarrow x = 50 \\
 \]
Hence the present ages of Ankita and Ajita are $ 50\;{\text{and}}\;20 $ years respectively.


Note: In the given question, the relation between Ankita's age and Ajita's age can be verified. If your answers are not satisfying the given conditions of the question, there may be errors in your equations. One can commit mistakes while writing the two different equations for defining the different relation between their ages ago five years and after ten years. Hence, carefully convert the word problems in the mathematical expressions which are the main aspect of solving these types of word problems.