On what dates of Aug 1980 did Monday fall?
Explanation:
Let us first calculate the day of the week on 1st August 1980.
Here we need to break days till 1st August 1980.
Complete years = 1979
Odd days in first 1600 years = 0 Odd days in next 300 years = 1 Odd days in next 79 years (19 leap and 60 non-leap years) = 19 × 2 + 60 × 1 = 98.
∴ Odd days in complete years = 0 + 1 + 98 = 99 odd days.
∴ Odd days in complete years = Remainder (99 ÷ 7) = 1 odd days.
Incomplete year (1980, a leap year)
Jan + Feb + Mar = 0 odd days, Apr + May + Jun = 0 odd days, Jul = 31 Aug = 1
∴ Odd days in incomplete year = 0 + 0 + 31 + 1 = 32 odd days = 4 odd days.
∴ Total odd days till 1st August 1980 = 1 + 4 = 5 odd days.
∴ Day of the week on 1st August 1980 will be 5 days after Sunday i.e., Friday.
Since 1st August 1980 is Friday, next Monday will be on 4th August.
Hence Mondays in August 1980 will be on 4th, 11th, 18th and 25th.
Hence, option (a).
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