Question

# Rakhi's mother is four times as old as rakhi. After 5 years. Her mother will be three times as old as she will be then. Find their present ages.

Hint: - Here we go through by supposing the age of rakhi be x then the mother age becomes 4x as given in the question. Then calculate accordingly to the question for finding the value of x.

Let the age of rakhi =x years
And according to the question it is given that mother age is four times the age of rakhi.
So the age of rakhi’s mother =4x years.
After 5 years
Age of rakhi =x+5 years
Age of mother =4x+5 years.
Now according to the second condition of question after five years. Her mother will be three times as old as rakhi.
$\Rightarrow 4x + 5 = 3(x + 5) \\ \Rightarrow 4x + 5 = 3x + 15 \\ \Rightarrow 4x - 3x = 15 - 5 \\$
$\therefore x = 10$
Hence the present age of rakhi = x years =10 years and
the age of Rakhi’s mother= 4x years = $4 \times 10 = 40$years.

Note: - Whenever we face such type of questions on age problems, first always suppose the present age in some variables and then apply the conditions of the question on that variable to find out the value of that variable to find out the result.