Option on adding Passengers Automatically

I am a travel agent and I want to create a form so that Passengers can add their details in the form.

I wanted to know if there was an option or widget for the customer to add more passengers themselves by clicking on a button and the same passenger page gets duplicated.

Therefore, they will be able to add as many as they wish. 

Although your requirement can be achieved using the conditional logics Show/Hide a Field and/or Skip/Hide to a Page 

How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

Hide-or-Show-Multiple-Fields-at-Once

How-to-skip-pages-using-conditional-logic

I believe it can still be best achieved if you use the Configurable List widget.

How-to-Set-Up-the-Configurable-List-Widget

How-to-Style-Change-the-Layout-and-Customize-the-Configurable-List-Widget?

When using conditions to show the same set of fields, the number of sets can be limited based on the number of sets you create in your form. However, when using the Configurable List widget the sets can be unlimited.

How-to-Add-a-Widget-to-your-Form