300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Let the total number of students be x

According to the question

taking LCM

cross multiplying

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = 10 c = – 3000

= 1. – 3000 = – 3000

And either of their sum or difference = b

= 10

Thus the two terms are 60 and – 50

Difference = 60 – 50 = 10

Product = 60. – 50 = – 3000

x^{2} + 60x – 50x – 3000 = 0

x(x + 60) – 50(x + 60) = 0

(x + 60) (x – 50) = 0

(x – 50) = 0 or (x + 60) = 0

x = 50 or x = – 60

x cannot be negative thus total number of students = 50

30