Problem Solving

IN A CLASS OF 30 STUDENTS, 2 STUDENTS DID NOT BORROW ANY BOOKS FROM THE LIBRARY, 12 STUDENTS EACH BORROWED 1 BOOK, 10 STUDENTS BORROWED 2 BOOKS AND THE REST OF THE STUDENTS BORROWED AT LEAST 3 BOOKS. IF THE AVERAGE (MEAN) NUMBER OF BOOKS BORROWED PER STUDENT WAS 2 , WHAT IS THE MAXIMUM NUMBER OF BOOKS THAT ANY SINGLE STUDENT COULD HAVE BORROWED?

- 3
- 5
- 8
- 13
- 15

ANSWER IS 13. CAN ANYONE SHOW ME HOW TO SOLVE THIS? THANKS

Here is the explaination

Step 1)
Avg no. of book for the whole class is 2
Total no of students is 30
So total no. of books borrowed is =30*2 =60

Now check other info you have

1) 2 students - 0 Books
2) 12 students - 1 book each = 12 Books
3) 10 students - 2 books each = 20
3) Remaining 6 students have min 3 books each

In order to maximise the no of books for 1 person you have to minimise the books taken by remaining students

You can do this by assuming 5 of the remaining 6 students took the min permissible books = 3

So total = 5*3 =15

Now add all taken out = 12+20+15 =47

But in all 60 books were taken out (see step 1)

So max books final person could take is 60 - 47 =13