Question

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

Answer 1

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

Number of students come by car $=\frac{2}{5}\times x=\frac{2}{5}x$

Number of students come by bus $=\frac{1}{4}\times x=\frac{1}{4}x$

Remaining students walk to school

$=x-(\frac{2}{5}x+\frac{1}{4}x)=x-\left(\frac{8x+5x}{20}\right)$

$=x-\frac{13x}{20}=\frac{20x-13x}{20}=\frac{7x}{20}$

Now, number of students walk to school on their own

$=\frac{1}{3}$ of $\frac{7x}{20}=\frac{7x}{60}$

Since, $224$ students come to school on their own.

According to the question

$\Rightarrow \frac{7x}{60}=224$

$\Rightarrow x=\frac{224\times 60}{7}$

$\Rightarrow x=32\times 60=1920$

Hence, $1920$ students study in that school.