300 chocolates are distributed equally among a certain number of students. Had there been 10 more students, each would have received one chocolate less. The number of students is ___ .

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Solution

The correct option is A
50

Let the number of students be x

Number of chocolates each student gets = $\frac{300}{x}$

Number of chocolates each student gets when there are 10 more students = $\frac{300}{x + 10}$

then $\frac{300}{x} - \frac{300}{x + 10} = 1 \frac{300 (x + 10) - 300 x}{x (x + 10)} = 1 x^{2} + 10 x - 3000 = 0 x^{2} + 60 x - 50 x - 3000 = 0 x (x + 60) - 50 (x + 60) = 0 (x + 60) (x - 50) = 0 \Rightarrow x = - 60 o r x = 50 ∴ n u m b e r o f s t u d e n t s = 50$

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