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 $\frac{s}{c+1} = 20 \Longrightarrow s = 20c + 20$ $\frac{s}{c-1} = 30 \Longrightarrow s = 30c - 30$

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

~Bradygho

Solution 2

We have the number of classes is $x$ , so $20(x+1)=30(x-1)$ , or $x=5$ . Plugging back the total number of students is $120$ , so the answer is $\frac{120}{5} = \boxed{24}$ $\linebreak$ ~Geometry285

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2021 JMPSC Accuracy Problems/Problem 10

Problem

Solution

Solution 2