Two years ago Tom was $25\%$ shorter than Mary. Since then Tom has grown $20\%$ taller, and Mary has grown $4$ inches taller. Now Mary is $20\%$ taller than Tom. How many inches tall is Tom now?
1. Let \( t \) be Tom's height two years ago and \( m \) be Mary's height two years ago. According to the problem, two years ago Tom was \( 25\% \) shorter than Mary. This can be written as:
   \[
   t = 0.75m
   \]

2. Since then, Tom has grown \( 20\% \) taller. Therefore, Tom's current height is:
   \[
   1.2t
   \]

3. Mary has grown \( 4 \) inches taller. Therefore, Mary's current height is:
   \[
   m + 4
   \]

4. Now, Mary is \( 20\% \) taller than Tom. This can be written as:
   \[
   m + 4 = 1.2(1.2t)
   \]

5. Substitute \( t = 0.75m \) into the equation:
   \[
   m + 4 = 1.2(1.2 \cdot 0.75m)
   \]

6. Simplify the right-hand side:
   \[
   m + 4 = 1.2 \cdot 0.9m
   \]
   \[
   m + 4 = 1.08m
   \]

7. Solve for \( m \):
   \[
   m + 4 = 1.08m
   \]
   \[
   4 = 1.08m - m
   \]
   \[
   4 = 0.08m
   \]
   \[
   m = \frac{4}{0.08}
   \]
   \[
   m = 50
   \]

8. Now, substitute \( m = 50 \) back into \( t = 0.75m \) to find Tom's height two years ago:
   \[
   t = 0.75 \cdot 50
   \]
   \[
   t = 37.5
   \]

9. Tom's current height is \( 1.2t \):
   \[
   1.2t = 1.2 \cdot 37.5
   \]
   \[
   1.2t = 45
   \]

The final answer is \(\boxed{45}\) inches.