So when you click on Diversity, you want the other worksheet to show? One way you can do this is by using a menu action.
Are you able to post a sample workbook (twbx file)?
Yes, very possible, and something Tableau is great for (interaction in visualizations).
As Tracy said, the approach you'll want is likely to include using Dashboard actions. The percentages would be in one sheet, and whatever result you are looking for would be contained in a separate sheet (or sheets). Plop them on the dashboard together, and create your action filter(s) to coordinate the results you want. You'll want to include fields in both sheets that are used for linking, so Tableau can connect the action based on a common field.
This one also has a nice Example with the "Select a Sub Category": Creating Filters with Actions on Dashboards | Tableau Software
I tried and could set an action to show the breakup of diversity in the above example on a separate dashboard. My question is When the user lands on the main dashboard, the diversity breakup should not be visible. It should become visioble only when user click on the Diversrity or its percentage.
There is an option to "Exclude All Values" when the action is cleared. So, if you use the action, and then clear it, and then save/publish the workbook in the state, the sheet will be blank until something is clicked. However, that will clear the entire sheet so if all those different values are on one sheet, they'll all be blank--to get around this, you could put each of the figures in separate worksheets, with separate actions for each, and then using the "Exclude..." option would work for you. This is what I'd do.
There may be another workaround, but its certainly doable.