Question

At an annual function of a school, each student gives gift to every other student. If the number of gifts is 1980 find the number of students.

Answer 1

Let the number of students be x.

Given that each student gives a gift to every other student.

That means the number of ways in which each child gives a gift to every other child = x(x - 1).

Given that total number of gifts = 1980

x(x - 1) = 1980

x^2 - x = 1980

x^2 - x - 1980 = 0

x^2 - 45x + 44x - 1980 = 0

x(x - 45) + 44(x - 45) = 0

(x + 44)(x - 45) = 0

x = 45 (or) x = -44.


Since x cannot be -ve, So x = 45.


Therefore the number of students = 45