api controller not being called correctly in a Published iis hosted mvc 5 application

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IIS8

MVC5

I have hosted mvc 5 application in iis,
Normal controller pages work fine,
but if there are any web api being used , the api is not called correctly, it throws a 404 error.

For ex : My application is located at http://localhost/Publish folder.

Please suggest why is the api path not being recognised as expected.
The browser is checking for an api at : http://localhost/api/chartsapi/3
but it is not able to get this so it shows 404.
But the api is located at : http://localhost/Publish/api/chartsapi/3.

But this works fine in local

Please Suggest.