# CAT Practice : Averages, Ratios, Mixtures

We need to find out the share of the other students first! Their share plus 1/6th is total share, from which we can find the total number of students...

## Number of students

Q.21: 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?
1. 30
2. 26
3. 11
4. 31

Choice B. 26

## Detailed Solution

Let the total students be (n + 1)
Let the average of ‘n’ students be y

The student who got 1/6th of x = 5y
Or y = x/30

Therefore ‘n’ students got 1/30th of total share each
Or n * x/30 + 1 * x/6 = x
nx + 5x = 30x
n + 5 = 30
Or n = 25
Total = n + 1 = 26

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