As of the end of May, 42,075 couples in Beijing had submitted applications, 38,798 of which had been approved.
Among those approved, 57 per cent of the potential mothers were aged between 31 and 35 years old, according to Beijing's Commission of Health and Family Planning.
In February, the commission suggested that the new policy would increase Beijing's population by an expected 270,000, around 54,000 extra births each year until 2019 when the figure should begin to return to normal.
About 1.45 million couples across the whole country, around 13 per cent of those eligible, had applied for a second baby by the end of May.
A major policy change was adopted at the end of 2013, stipulating that couples nationwide could have a second child if either parent was an only child.
The adjustment, however, was put into practice in early 2014.
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