Account is parent object of Case. Case’s status field is categorized into two types – Open or closed which can be tracked by field “IsClosed”.
On Account, there is a checkbox field “Has Open Case”, if there is any open Case under account, this field should be checked. Please make sure all scenarios ate covered.
Upload your code in Github and provide the link of public repo in comment below, it will be reviewed based on availability and feedback will be shared.
P.S: Be honest, watch the clock to check your efficiency. Happy coding.