Q:

Is there a web-based API available to find User's TimeZone based on his/her Tel countrycode?

I do require an API (preferably RESTful), to find the timezone of a dialed number (e.g. +44xxxvvvyyyy (UK) = GMT etc) for an academic project. I thought there might be an API available somewhere that stops me to write the service and make it available myself !! I am well aware of the issues the service should address with regards to multi-zoned countries like US and Russia. 
Any help would be appreciated in advance.

A:

Googling 'telephone country code web service' came back with:
https://restcountries.eu
In particular, what you were looking for:
https://restcountries.eu/rest/v1/callingcode/
Australia:
https://restcountries.eu/rest/v1/callingcode/61
[
    {
        "name": "Australia",
        "capital": "Canberra",
        "altSpellings": [
            "AU"
        ],
        "relevance": "1.5",
        "region": "Oceania",
        "subregion": "Australia and New Zealand",
        "translations": {
            "de": "Australien",
            "es": "Australia",
            "fr": "Australie",
            "ja": "オーストラリア",
            "it": "Australia"
        },
        "population": 23868800,
        "latlng": [
            -27,
            133
        ],
        "demonym": "Australian",
        "area": 7692024,
        "gini": 30.5,
        "timezones": [
            "UTC+05:00",
            "UTC+06:30",
            "UTC+07:00",
            "UTC+08:00",
            "UTC+09:30",
            "UTC+10:00",
            "UTC+10:30",
            "UTC+11:30"
        ]
        ...

