Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?

Sure, let's solve this step by step:

1. Let's denote the present age of X as x and the present age of Y as y.

2. According to the problem, twice the age of X is thrice the age of Y. We can write this as: 2x = 3y.

3. The problem also states that 8 years ago, the difference between the ages of X and Y was 18 years. We can write this as: (x-8) - (y-8) = 18.

4. Now we have a system of two equations: 2x = 3y and x - y = 18 + 8 = 26.

5. We can solve this system of equations. Let's start with the second equation: x = y + 26.

6. Now we can substitute x in the first equation: 2(y + 26) = 3y.

7. This simplifies to 2y + 52 = 3y.

8. Solving for y, we get y = 52.

9. Substituting y = 52 in the equation x = y + 26, we get x = 52 + 26 = 78.

So, the present age of X is 78 years.