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

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answer is A.

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Detailed Solution

Given that 300 apples are distributed equally among a certain number of students.
Let the number of students be p.
According to the given condition,
300 apples are distributed equally among p students then one student get,

= \frac{300}{p}

Apples -1)
Later 10 students were added. So, one student gets,

= \frac{300}{p + 10}

Apples -2)
According to question when 10 more students added, each would have received one apple less then we can write,

\frac{300}{p} - \frac{300}{p + 10} = 1

⟹ \frac{300 (p + 10) - 300 p}{p (p + 10)} = 1

⟹ \frac{300 p + 3000 - 300 p}{p^{2} + 10 p} = 1

⟹ 3000 = p^{2} + 10 p

⟹ p^{2} + 10 p - 3000 = 0

⟹ p^{2} + 60 p - 50 p - 3000 = 0

⟹ p (p + 60) - 50 (p + 60) = 0

⟹ (p + 60) (p - 50) = 0

⟹ p + 60 = 0 or            p - 50 = 0

∴ p = - 60 or                       p = 50

The total number of students is 50.
Hence, the correct option is 1.

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