Question

$300$ 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.

• A. Number of students: $70$
• B. Number of students: $90$
• C. Number of students: $50$
• D. Number of students: $40$

Answer 1

The correct option is C Number of students: $50$

Let the number of students be $x$.

Then, the number of apples received by each student is $\frac{300}{x}$.If there are $10$ more students, i.e. $(x+10)$ students.

Then, the number of apples received by each student is $\frac{300}{x+10}$.

According to the question,

$\frac{300}{x}-\frac{300}{x+10}=1$

$\Rightarrow \frac{300x+3000-300x}{x(x+10)}=1$

$\Rightarrow 3000=x^2+10x$

$\Rightarrow x^2+10x-3000=0$

$\Rightarrow x^2+60x-50x-3000=0$

$\Rightarrow x(x+60)-50(x+60)=0$

$\Rightarrow (x+60)(x-50)=0$

$\Rightarrow x=-60$ or $x=50$

But the number of students can not be negative.

Hence, the number. of students is $50$.