Question

In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought at least one book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer then what could be the total number of books brought by the remaining students?

• A. 12
• B. 16
• C. 14
• D. 8

Answer 1

The correct option is A 12

Total number of Students $=20$

10 boys brought $11books$ each

Total books brought by 10 boys $=11\times 10=110$

$6girls$ brought $13books$ each.

Total books brought by $6girls=6\times 13=78$

Average number of books are $positive$ integers.

Total books brought by $10boys$ & $6girls$ $=110+78=188$

For average positive integers number of books greater than $188$ and

also multiple of $20$.

Total number of books $=200$

Total books brought by remaining students $=200-188=12Ans.$