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# Vikas is three years older than Deepika. Six years ago, Vikas’s age was four times Deepika’s age. Find the ages of Deepika and Vikas.  Verified
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Hint:
Take the age of Deepika as ‘x’ and that of Vikas as ‘x+3’. From the present age subtract 6, to get their age 6 years ago. Now 6 years ago Vikas’s age was 4 times Deepika’s age. Find the expression and solve it to get the present age of Vikas and Deepika.

Let us consider the age of Deepika as ‘x’ years old. And let the age of Vikas be (x + 3) years, as it is mentioned that Vikas is three years older than Deepika.
Now let us consider the case dating back 6 years ago.
Let us consider the age of Deepika 6 years ago as the present age ‘x’ minus 6 years.
$\therefore$Age of Deepika = x – 6.
The age of Vikas 6 years ago as the present age of Vikas minus 6 years.
$\therefore$Age of Vikas = x + 3 – 6 = x – 3.
It is given in the question that Vikas age is 4 times that of Depika’s age.
$\therefore$ Age of Vikas 6 years ago =$4\times$age of Deepika 6 years ago.
$\Rightarrow \left( x-3 \right)=4\left( x-6 \right)$
Open the brackets and simplify the expression.
\begin{align} & x-3=4x-24 \\ & \Rightarrow 4x-x=24-3 \\ & \therefore 3x=21 \\ & x=\dfrac{21}{3}=7 \\ \end{align}
We got the present age of Deepika as 7 years old.
$\therefore$Age of Vikas = x + 3 = 7 + 3 = 10 years old.
$\therefore$Present age of Deepika = 7 years.
Present age of Vikas = 10 years.

Note:
We can solve this question in a tabular form, considering their present age and their age 6 years ago.

 Present Age Age 6 years ago Deepika x x-6 Vikas x+3 x+3 -6=x-3

Given that the Age of Vikas was four times the age of Deepika 6 years ago.
So take the 2nd column,
$\left( x-3 \right)=4\left( x-6 \right)$
$\Rightarrow x=7$i.e. the age of Deepika.
$x=7+3=10$, the age of Vikas.