Question

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

Answer 1

Hint: Assume the total number of students of the school as a variable. Generate equations from the given information, solve for the variable, and get the desired answer.

Complete step-by-step answer:

Let the total number of students study in the school is x. Now, it is given that \[\dfrac{2}{5}\] of the total number of students of a school come by a car while \[\dfrac{1}{4}\] come by bus to school.
So, number of students coming by car to school = \[\dfrac{2x}{5}\] and, number of students coming by bus to school = \[\dfrac{x}{4}\]
So, the number of rest of the students = \[x-\left( \dfrac{2x}{5}+\dfrac{x}{4} \right)\] = \[\dfrac{7x}{20}\]
Now it is given that among the other entire students walk to school of which \[\dfrac{1}{3}\] walk on their own and their parents escort the rest.
So, number of students walk to school = \[\dfrac{7x}{20}\cdot \dfrac{1}{3}=\dfrac{7x}{60}\]
So, according to the given problem,\[\dfrac{7x}{60}=224\]
\[\Rightarrow x=\dfrac{224\cdot 60}{7}=1920\]
So the total number of students is 1920.
Hence, the total number of students studying in that school is 1920.

Note: It is not mandatory to assume a variable. Just take the fractions and which sums up to 1. This method will also lead to this result.