$\dfrac{2}{5}$ of total number of students of a school come by a car, while $\dfrac{1}{4}$ of students come by bus to school. All the other students walk to school, of which $\dfrac{1}{3}$ walk on their own and rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in that school?

1. 2000

2. 1970

3. 1920

4. 1904

First find the fraction of the students who walk on their own, then use it to find the total number of students.

Finding the fraction of the students who come by car or by bus,

LCM of 5 and 4 = 20

$\dfrac{2}{5} + \dfrac{1}{4} = \dfrac{2 \times 4 + 1 \times 5}{20} \\[1em] = \dfrac{8 + 5}{20} = \dfrac{13}{20}$

Finding the fraction of the students who walk to school,

$1 - \dfrac{13}{20} = \dfrac{20 - 13}{20} = \dfrac{7}{20}$

Finding the fraction of the students who walk on their own,

$\dfrac{1}{3} \times \dfrac{7}{20} = \dfrac{7}{60}$

Let the total number of students in the school be $x$.

$\Rightarrow \dfrac{7}{60} \times x = 224 \\[1em] \Rightarrow x = 224 \times \dfrac{60}{7} \\[1em] \Rightarrow x = 32 \times 60 \\[1em] \Rightarrow x = 1920$

Hence, Option 3 is the correct option.