If the 19th of June 2001 is Tuesday, what will be the day of the week on the 21st of August 2009?

Friday

19th of June 2001 is Tuesday,

-> Number of days from 19 June 2001 to 31 December 2001 => 11 + 31 + 31 + 30 + 31 + 30 + 31 = 195

-> Number of days from 1 January 2002 to 31 December 2008 => (7 × 365) + 2 = 2557 (2 leap year)

-> Number of days from 1 January 2009 to 21 August 2009 => 31 + 28 + 31 + 30 + 31 + 30 + 31 + 21 = 233

So, the total number of days from 19 June 2001 to 21 August 2009 => 195 + 2557 + 233 = 2985

Now, on dividing 2985 by 7, we get 426 as the quotient and 3 as the remainder.

Thus, add 3 to Tuesday, Tuesday + 3 = Friday