Question

Vikas is threeyears older than Deepika.Six years ago,Vikas's age was four times Deepika's age.Find the ages of Deepika and Vikas

Answer 1

Given:

Vikas is three years older than Deepika. Six years ago, Vikas's age was four times Deepika's age.

To find:

The ages of Deepika and Vikas.

Solution:

Let the present age of Deepika be x years.

So, the present age of Vikas = x + 3 years

Six years ago,

The age of Deepika = x - 6 years

The age of Vikas = x + 3 - 6 years = x - 3 years.

Now,

according to the question, we have,

$x - 3 = 4(x - 6)$

After opening the brackets, we get

$x - 3 = 4x - 24$

On solving the above, we get

$3x = 21$

$x = 7 \: years$

which is the present age of Deepika.

So, the present age of Vikas = 7 + 3 = 10 years.

Hence, the present age of Deepika and Vikas is 7 years and 10 years respectively.

Answer 2

Given: Vikas is three years older than Deepika. Six years ago, Vikas's age was four times Deepika's age.

To find: The ages of Deepika and Vikas.

Solution:

Let the ages of Vikas and Deepika be x and y, respectively. According to the question, Vikas is three years older than Deepika. This statement can be written in the form of an equation as follows.

$x = 3+y$

$x-y=3$

Six years ago, their ages can be written as follows.

$Vikas = x-6$

$Deepika=y-6$

Now, according to the question, six years ago, Vikas's age was four times Deepika's age. Thus, this statement can be written in the form of an equation as shown below.

$x-6 = 4 (y-6)$

$x-4y = -18$

The two equations obtained can be solved simultaneously in order to find the value of x and y.

$x = 10$

$y=7$

Therefore, the ages of Vikas and Deepika are 10 and 7, respectively.