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By Rajesh Kumar Singh

NEW DELHI, Nov 30 (Reuters) - India has posted the world's fastest growth rate for a large economy in the September quarter, yet that offered cold comfort after misery inflicted by the government's shock move to remove high denomination banknotes from circulation.

Gross domestic product (GDP) data released on Wednesday showed Asia's third-largest economy expanded by 7.3 percent on year between July and September, faster than a provisional 7.1 percent growth in the previous quarter.

Economists polled by Reuters had expected a 7.5 percent expansion in the quarter.

Farm output grew 3.3 percent year-on-year during the quarter, faster than 1.8 percent in the quarter through June. Manufacturing slowed in the September quarter, posting an annual growth of 7.1 percent compared with 9.1 percent in the previous quarter.

India's growth rate overtook China in 2015 and has stayed ahead, thanks to reforms and stimulus undertaken by Prime Minister Narendra Modi since he swept to power 2-1/2 years ago.

But Modi's decision this month to scrap 500 rupee and 1,000 rupee banknotes as part of a crackdown on tax dodgers and counterfeiters has removed 86 percent of the currency in circulation virtually overnight.

In India, most people are paid in cash, and buy what they need with cash. The government's shock therapy has left companies, farmers and households suffering.

Economists agree the economy will take a hit this quarter and for several quarters to follow. But how bad depends on who is talking.

Finance Minister Arun Jaitley expects the cash crunch to have a minor impact lasting for a quarter or two. Private economists, however, reckon the impact would be felt through 2018.

The most optimistic forecasts suggest that India will finish this fiscal year in March with a respectable, but slightly lower, growth rate of 7.3 percent.

But the most pessimistic forecast, from Mumbai-based brokerage Ambit Capital, for a precipitous drop to 3.5 percent growth shows just how worried people are.

(Editing by Simon Cameron-Moore and Douglas Busvine) ((rajeshkumar.singh@thomsonreuters.com; +91-11-4954-8041; Reuters Messaging: rajeshkumar.singh.thomsonreuters.com@reuters.net))