Estonian Mathematical Olympiad

Question

A slider on the scrolling bar of Paul's mail client shows the proportion of emails which are preceding the email which is currently open. Paul noticed that before deleting some emails the slider was on 10%. Paul deleted some consecutive emails, starting from the one which was currently open. After that the slider was on 50%. What is the percentage of the emails that Paul deleted?

Accepted Answer

Let n be the number of emails before deletion. As the slider showed 10% before deletion there were 0.1n emails preceding the email that was open when Paul started the deletion. After the end of the deletion those emails accounted for 50% from the remaining emails which means that 0.2n emails remained in the inbox. Thus Paul deleted 0.8n emails which makes up 80% of the emails present in the inbox before deletion.