# 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.

Answer

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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.

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.

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.

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