A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got! How many students were there in the class?
Choose the correct choice from the following answers.
A) 30 B) 26 C) 11 D) 31 E) 32

Rationale: detailed solution let the total students be ( n + 1 ) let total badges be x let the average of ‘ n ’ students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore ‘ n ’ students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b
Answer: B