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The company’s financial performance in the quarter was also boosted by sales of the Apple Watch, record Mac sales and revenue from services.
Apple also reported record sales for the 2015 financial year of $234bn and net profit of $53.4bn, up by 35% from $39.5bn in 2014.
This is the biggest annual profit in corporate history, surpassing the $45.2bn made by ExxonMobil in 2008, according to the Telegraph.
The company said it sold 48 million iPhones in the quarter, a rise of 22% compared with the same period a year ago, and accounting for nearly 63% of the company's quarterly revenue.
Apple also claimed that as much as 30% of iPhone buyers were switching from Android devices.
Analysts said iPhone sales have helped offset the falling iPad sales, which declined by 20% in the quarter to nearly 10 million compared with the same period in 2014.
The exact number of Apple Watches sold in the quarter was not disclosed, but analysts put the figure at around 3.5 million.
Although this is still tiny in comparison with more established Apple products, it is currently considered to be the most successful smartwatch on the market.
Apple chief executive Tim Cook said 2015 is the company’s most successful fiscal year to date and that the figures augured well for the Christmas holiday season.
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“We are heading into the holidays with our strongest product lineup yet, including iPhone 6s and iPhone 6s Plus, Apple Watch with an expanded lineup of cases and bands, the new iPad Pro and the all-new Apple TV which begins shipping this week,” he said.
In China, the biggest market for smartphones, Apple's sales nearly doubled from a year ago to $12.52bn, although that is down by 5% compared with the previous quarter, reports the BBC.
For the current quarter, Apple expects global sales of between $75.5bn and $77.5bn.
Although the forecast is slightly below market expectations, analysts said investors were expecting a lower figure, which is why the stock initially rose by 3% in after-hours trading.