Question

Seven out of every 8 students surveyed owns a bicycle. The difference between the number of students who own a bike and those who do not is 72. How many students were surveyed?

Answer 1

The total number of students were surveyed is 96 students

Explanation:

The given is,

Seven out of every 8 students owns a bicycle

The difference between the number of students who own a bike and those who do not is 72.

Step: 1

Let, T - Total number of students were surveyed

X - Students who own a bike

Y - Students who do not bike

Step:2

From the given,

Ratio of Students own a bike is =
`(7)/(8)`

Ratio of students who do not own a bike is =
`(1)/(8)`

Step:3

X = Ratio of students who own bike × Total number of students

=
`(7)/(8)` × T

Y = Ratio of students who do not own bike × Total number of students

=
`(1)/(8)` × T

Step:4

From given, (∵ Difference is 72)

X-Y = 72

(
`(7)/(8)` × T) - (
`(1)/(8)` × T) = 72

0.875T - 0,125T = 72

0.75T = 72

T = 96 students.

Step:5

X =
`(7)/(8)` × T =
`(7)/(8)` × 96 = 84

Y =
`(1)/(8)` × T =
`(1)/(8)` ×96 = 12

Result:

The total number of students were surveyed is 96 students and 84 students have a own bike and 12 students do not have a own bike.