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Hi Rashmi and welcome to MySwissAlps.com!
So are you coming from Frankfurt, Germany? Then make sure to have a look at http://www.myswissalps.com/traintickets/germany, where you get tips on how to buy your tickets from Germany to Switzerland.
Yes, you will probably cross the border at Basel. I believe that the 50-60 CHF that you’ve found for the Basel-Zermatt trip is half price. The SBB timetable shows half prices by default, assuming that you already have a rail pass (like the Swiss Half Fare Card).
With a Saver Day Pass you can travel for free from Basel to Zermatt, but gives you no discount for the mountain transports (like cable cars). read more about the Saver Day Pass at http://www.myswissalps.com/saverdaypass. Make sure to check the ‘Where is it valid’ tab.
To be able to decide what pass is the best option for you, first you need to have your itinerary. From Zermatt you can visit Gornergrat or Klein Matterhorn or Sunnegga: http://www.myswissalps.com/zermatt.
I did not understand, are you staying in Zermatt 2 days + the traveling dates from and back to Frankfurt? If yes, then a Swiss Travel Pass (3 or 4 days) can be also good for you. With the Swiss Travel Pass you travel for free from Basel to Zermatt and you also get 50% discounts on mountain transport. More information about the Swiss Travel Pass: http://www.myswissalps.com/swisstravelpass (see the ‘Where is it valid’ part).
If you have only 2 days then Zermatt is enough for that, I would say.
Take care,
Ildiko