Question

$\frac{2}{5}$ of the 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

Find the number of students studying in that school.

Let the total number of students in the school be$\mathrm{N}$

Step 1: Find the number of students who walk to school.

According to the given details

The number of students come by car $=\frac{2}{5}\times \mathrm{N}$

The number of students come by bus $=\frac{1}{4}\times \mathrm{N}$

$\begin{array}{rcl}\mathrm{Remaining}\mathrm{students}\mathrm{walk}\mathrm{to}\mathrm{school}& =& \mathrm{N}–\left[\left(\frac{2\mathrm{N}}{5}\right)+\left(\frac{1\mathrm{N}}{4}\right)\right]\\ & =& \mathrm{N}–\left[\frac{8\mathrm{N}+5\mathrm{N}}{20}\right]\\ & =& \mathrm{N}–\left[\frac{13\mathrm{N}}{20}\right]\\ & =& \frac{20\mathrm{N}–13\mathrm{N}}{20}\\ & =& \frac{7\mathrm{N}}{20}\end{array}$

$\therefore$The number of students who walk to school is$\frac{7\mathrm{N}}{20}$.

Step 2: Find the number of students studying in that school or the value of $\mathrm{N}$

The number of students walking to school on their own $=\frac{1}{3}\mathrm{of}\frac{7\mathrm{N}}{20}$

$\begin{array}{rcl}224& =& \frac{7\mathrm{N}}{60}\\ 224\times 60& =& 7\mathrm{N}\\ \mathrm{N}& =& \frac{224\times 60}{7}\\ \mathrm{N}& =& 32\times 60\\ \therefore \mathrm{N}& =& 1920\end{array}$

Hence, the total number of students in that school is$1920$.