2021 JMPSC Accuracy Problems/Problem 10

Revision as of 22:29, 10 July 2021 by Bradygho (talk | contribs) (Solution)

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