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\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:

Let us assume total number of students in the school be x.

From the question it is given that,

The number of students come by car = \frac{2}{5} × x

The number of students come by bus = \frac{1}{4} × x

Remaining students walk to school = x-\frac{2x}{5}+(\frac{1}{4}x)\ =\ x-\frac{(8x+5x)}{20}\ =\ x-\frac{13x}{20}=\frac{(20x-13x)}{20}=\frac{7x}{20}

Then, 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.

As per the data given in the question,

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

x =\frac{(224\times60)}{7}

x = 32 × 60

x = 1920

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

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