Question

Muskaan is twice as old as Khushi. Five years ago, her age was three times of Khushi’s age. Find their present ages.

Answer 1

We solve this question by writing the given information as equations. Then we assume the age of Muskaan and Khushi as $x$ and $y$. Then we substitute $x$ and $y$ in place of the age of Muskaan and age of Khushi. Then we solve the two equations and find the value of $x$ and $y$.

Complete step-by-step answer :
First let us consider the given statements in the question.
We are given that Muskaan is twice as old as Khushi, that is,
Age of Muskaan = 2(Age of Khushi)
Five years ago, the age of Muskaan was three times the age of Khushi.
Age of Muskaan = 3(Age of Khushi)

Let us assume the present age of Muskaan as $x$ and present age of Khushi as $y$.
Then we can write Age of Muskaan = 2(Age of Khushi) as,
$x=2y.......\left( 1 \right)$
Five years ago, their ages will be,
Age of Muskaan = x-5
Age of Khushi = y-5
Then we can write Age of Muskaan = 3(Age of Khushi) as,
$\begin{aligned} & \Rightarrow x-5=3\left( y-5 \right) \\\ & \Rightarrow x-5=3y-15 \\\ & \Rightarrow x=3y-10.........\left( 2 \right) \\\ \end{aligned}$
Now let us compare the equation (1) and equation (2). Then we get,
$\begin{aligned} & \Rightarrow 2y=3y-10 \\\ & \Rightarrow y=10 \\\ \end{aligned}$
Substituting this value in equation (1) we get,
$\Rightarrow x=2\left( 10 \right)=20$
So, we get the values of x and y as 20 and 10 respectively, that is,
Age of Muskaan = 20 years
Age of Khushi = 10 years
Hence the answer is 20 years, 10 years.

Note : We can also solve this question by assuming their ages before five years as $x$ and $y$. Then their present ages become $x+5$ and $y+5$. But the problem in taking as above is one might give the values of x and y we get after solving the present ages of Muskaan and Khushi, which is wrong. As their present ages are $x+5$ and $y+5$ we need to add 5 to the obtained values of x and y in this case. So, it is better to choose the values that we require for answers as x and y so that we get exact values and make no mistakes.