Question

Rakhi’s mother is four times as old as Rakhi. After $ 5 $ years her mother will be three times as old as she was then. Find their present ages.

Answer 1

Hint: In this type of age dependent problem we first let present age of Rakhi’s as ‘x’ and then calculate her mother age in term of ‘x’ and then forming an equation according to their ages after five years and solving it to get value of ‘x’ and so ages of Rakhi and her mother.

Complete step-by-step answer:
Let present age of Rakhi is = x
Then, present age of her mother = $ 4x $
Age of Rakhi after $ 5\,years $ = $ \left( {x + 5} \right)\,years $
Her mother age after $ 5\,years $ = $ \left( {4x + 5} \right)\,years $
But according to the question. Age of her mother after $ 5\,years $ will be three times the age as she was then.
Therefore, we have:
 $
  4x + 5 = 3\left( {x + 5} \right) \\
   \Rightarrow 4x + 5 = 3x + 15 \\
   \Rightarrow 4x - 3x = 15 - 5 \\
   \Rightarrow x = 10 \;
  $
Hence, the present age of Rakhi is $ 10\,years $ and the present age of her mother is $ 40\,years. $

Note: In age problems we first see is there any dependent person whose age can be calculated in terms of other person age. We first calculate the age of given persons and then form an equation as per given condition and on solving to get the required solution to the given problem.