There is a cycle race going on in a circular track and `1/5`th of the total in front a person and `5/6`th of the total behind that person gives up the total number of participants. How many participants are there?

Options

A. 25
B. 31
C. 30
D. 35

Answer

B

Explanation

Let the total number of participants in the cycle race =x
So, there are (x - 1) persons other than him.
[`because (x - 1) ` persons are before and also behind the person as it is a circular race.]
So, according to the question
`1/5 (x-1)+ 5/6(x - 1) = x `
or, `(6x – 6 + 25x – 25)/30 = x`
or `31x - 31 = 30x `
or, `x= 31 `
Therefore, the total number of participants in the cycle race = `x = 31`.