If ‘JANUARY’ is ‘JULY’, ‘SEPTEMBER’ is ‘SEPTEMBER

If
‘JANUARY’ is ‘JULY’,
‘SEPTEMBER’ is ‘SEPTEMBER,
‘FEBRUARY’ is ‘AUGUST’ and
‘MARCH’ is ‘MAY’
then ‘AUGUST’ is ?

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The Logic is :
January has 7 Letters and 7th month is July.
September has 9 Letters and 9th month is September.
February has 8 Letters and 8th month is August.
March has 5 Letters and 5th month is may.
Hence,
August is June
Since August has 6 Letters and 6th month is June.