Question

In a class of 15 students, on an average, each student got 12 books. If exactly two students received same number of books, and remaining student books average be an integer then which of the following could be the number of books received by each of the two students who received same number of books?
(1) 11
(2) 15
(3) 20
(4) 25

Answer 1

20 is your answer
........

Answer 2

Answer:

This question can be solved by elimination method.

First, 15 students get average of 12 books each.

So, lets assume the total number of books = 15 * 12 = 180

(Assuming that each of the 15 students get 12 books each).

Now, it is given that two students got equal books.

Lets take that the two students who got equal books are 11.

So, they take away 22 books. Now the books left are 180-22 = 158

158 books are to be distributed among 13 people.

158/13 = 12.15, which is not an integer. Hence, this option is eliminated.

Now, take option (4).

Let each of the student with equal books get 25 book each. So, they take away 50 books. Now, 130 books are left and are to be distributed among 13 students.

so, the average is 130/13 = 10, which is an integer.

Hence, the answer is option (4), that is 25.