Pawan is twice as old as ruby .

3years ago he was 3 times as old as ruby .how old is pawan now

Ruby now ---- x

Pawan now --- 2x

3 years ago:
Ruby --- x-3
Pawan -- 2x-3

2x-3 = 3(x-3)

carry on

2x-3= 3(x-3)

2x-3=3x-9
2x-3x= -9+3
-x= -6
Subtraction sign will cancel.
Therefore, x=6 remains.
Ruby age = x = 6 years.
And pawan age = 2x = 2×6 = 12years

Let's break down the given information step-by-step:

Let's assume Ruby's age as "x" years.
According to the first statement, Pawan is twice as old as Ruby.
So, Pawan's age would be 2x years.

According to the second statement, 3 years ago, Pawan was 3 times as old as Ruby.
So, 3 years ago Ruby's age was (x - 3) years, and Pawan's age was (2x - 3) years.

Therefore, we have the equation: (2x - 3) = 3(x - 3).

Let's solve the equation:
2x - 3 = 3x - 9
-x = -6
x = 6

Now, we know Ruby's age is 6 years. Plugging this value into the equation we found earlier, Pawan's current age is:
2x = 2 * 6 = 12 years.

Therefore, Pawan is currently 12 years old.

To find out how old Pawan is now, we'll need to use algebraic equations based on the given information.

Let's assume Ruby's age is represented by R.
According to the given information, Pawan is twice as old as Ruby, so Pawan's age is 2 times Ruby's age, which can be represented as 2R.

Now, three years ago, Pawan's age was Pawan's current age minus 3, which gives us 2R - 3.
Similarly, three years ago, Ruby's age was Ruby's current age minus 3, which gives us R - 3.

According to the problem, three years ago, Pawan was three times as old as Ruby, so we can set up the equation:

2R - 3 = 3(R - 3)

Let's solve this equation:

2R - 3 = 3R - 9
Subtracting 2R from both sides:
-3 = R - 9
Adding 9 to both sides:
6 = R

So, Ruby is 6 years old. To find out Pawan's age, we substitute Ruby's age (R = 6) into the equation for Pawan's age:

Pawan's age = 2R = 2(6) = 12

Therefore, Pawan is currently 12 years old.