Question

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

Answer 1

Answer: The answer is 50.

Step-by-step explanation:  Given that there are total 300 oranges which are distributed equally among the students.

Let 'n' be the number of students and 'x' be the number of oranges that each student get. Then,

$n\times x=300.$

Also, it is given that if the number of students increases by 10, then each student will get 1 orange less than before, so

$(n+10)\times (x-1)=300\\\\\Rightarrow nx-10+10x-n=nx\\\\\Rightarrow 10x-n-10=0\\\\\Rightarrow 10x-\dfrac{300}{x}-10=0\\\\\Rightarrow x^2-x-30=0\\\\\Rightarrow (x-6)(x+5)=0.$

This will give x = 6 or x = - 5.

Since number of oranges cannot be negative, so  x = 6.

Hence, the number of students is

$n=\dfrac{300}{5}=50.$

Thus, the answer is 50.