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Darjeeling is situated in West Bengal State whereas Pelling is in western Sikkim. The total distance is about 73 kms, but due to the hilly terrain it takes about 4.5 hours to reach by car from Darjeeling to Pelling.
Unfortunately there are no direct buses(gov. or private) on this route.
Although, You can get limited shared jeeps from Darjeeling(Chowk bazaar area). The small reserved cab fare is about Rs. 3,800/-. As these jeeps are available on sharing basis it's less likely to follow a proper time-table.