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NCERT Exemplar Solutions Class 8 Mathematics Solutions for Rational Numbers - Exercise in Chapter 1 - Rational Numbers
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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?
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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