Two-fifth of the students of a school go to school by bus, One-fourth by car and the remaining walk down to school. One-third of those who walk to school are not accompanied by any one, the rest are escorted by their parents. If 224 students walk to school on their own, what is the total number of students in the school?

Given:

One-fourth by car and the remaining walk down to school.

One-third of those who walk to school are not accompanied by anyone, the rest are escorted by their parents.

224 students walk to school on their own.

Let the total number of students be "x".

Two-fifth of the students of a school go to school by bus = (2/5)x

Number of students who walk to school = x - (2/5)x - (1/4)x

1/3 of the students who walk to school are not accompanied by anyone.

Number of students who are not accompanied = 1/3 × (x - (2/5)x - (1/4)x)

Calculations:

According to Question:

1/3 × (x - (2/5)x - (1/4)x) = 224

1/3 × (20x/20 - 8x/20 - 5x/20) = 224

1/3 × (7x/20) = 224

7x/60 = 224

x = 224 × 60 / 7

x = 1920

∴ The total number of students in the school is 1920.