2021 JMPSC Accuracy Problems/Problem 10

Problem

In a certain school, each class has an equal number of students. If the number of classes was to increase by $1$ , then each class would have $20$ students. If the number of classes was to decrease by $1$ , then each class would have $30$ students. How many students are in each class?

Solution

Let the number of total students by $s$ , and number of classes by $c$ . Thus, our problem implies that $\frac{s}{c+1} = 20 \rightarrow s = 20c + 20$ $\frac{s}{c-1} = 30 \rightarrow s = 30c - 30$

We solve this system of linear equations to get $c = 5$ and $s = 120$ . Thus, our answer is $\frac{s}{c} = \boxed{24}$ .

~Bradygho

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2021 JMPSC Accuracy Problems/Problem 10

Problem

Solution