The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?
1. Let \( F \) be the number of freshmen, \( S \) be the number of sophomores, \( J \) be the number of juniors, and \( R \) be the number of seniors.
2. We are given that there are 144 sophomores, so \( S = 144 \).
3. We are also given that there are 10 percent fewer sophomores than freshmen. Therefore, \( S = 0.9F \). Solving for \( F \):
   \[
   144 = 0.9F \implies F = \frac{144}{0.9} = 160
   \]
4. There are 25 percent more freshmen than juniors. Therefore, \( F = 1.25J \). Solving for \( J \):
   \[
   160 = 1.25J \implies J = \frac{160}{1.25} = 128
   \]
5. We are given that 20 percent of the students are seniors. Let \( T \) be the total number of students. Therefore, \( R = 0.2T \).
6. The total number of students is the sum of freshmen, sophomores, juniors, and seniors:
   \[
   T = F + S + J + R
   \]
7. Substituting the known values:
   \[
   T = 160 + 144 + 128 + 0.2T
   \]
8. Solving for \( T \):
   \[
   T - 0.2T = 160 + 144 + 128 \implies 0.8T = 432 \implies T = \frac{432}{0.8} = 540
   \]

The final answer is \(\boxed{540}\).