Step 1: Count years and leap years between the two dates.
From 1 Jun 1981 to 1 Jun 2013 is 32 years. Leap years in this span (inclusive of 2012, exclusive of 1980):
1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012 — 8 leap years.
Step 2: Day shift.
Each ordinary year shifts the weekday by +1 day; each leap year by an additional +1 day.
Total shift = 32 + 8 = 40 days.
40 mod 7 = 5 — going back 5 days from Saturday (because 1981 is earlier):
Saturday → Friday (1) → Thursday (2) → Wednesday (3) → Tuesday (4) → Monday (5).
Answer:
Monday