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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.

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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.

Complete step-by-step answer:
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.