Question

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

Answer 1

Let the number of students = x
then the number of gifts given = x – 1
Total number of gifts = x (x – 1)
According to the condition,
x (x – 1) = 1980
⇒ x² - x - 1980 = 0
⇒ x² - 45x + 44x - 1980 = 0
⇒ x(x - 45) + 44(x - 45) = 0
⇒ (x - 45)(x + 44) = 0
Either x - 45 = 0,
then x = 45
or
x + 44 = 0,
then x = -44,
but it is not possible as it is negative.
Hence number of students = 45.