In the particular year 12th January is a Sunday, then which one of the following is correct? 15th July is a Sunday if the year is a leap year. 15th July is a Sunday if the year is not a leap year. 12th July is Sunday if the year is a leap year. 12th July is a not Sunday if the year is a leap year.

In the particular year 12th January is a Sunday

In the particular year 12th January is a Sunday, then which one of the following is correct?

Answer: C

Method I:

12th January is Sunday. If it is not a leap year, then:

Days between 15th July and 12th January = (31 - 11) + 28 + 31 + 30 + 31 + 30 + 14 = 184

Odd days = Remainder (184/7) = 2

So, day on 15th July if that year is a non-leap year = Sunday + 2 = Tuesday

If it was a leap year, then we need to take into account one extra day in the month of February, i.e. 29th February.

So, day on 15th July if that year is a leap year = Sunday + 3 = Wednesday

Similarly, the day on 12th July (non-leap year) = Day on 15th July - 3 = Tuesday - 3 = Saturday

The day on 12th July (leap year) = Day on 15th July - 3 = Wednesday - 3 = Sunday

Method II:

Just count the odd days.

Odd days in January = Remainder [(31 - 11)/7] = Remainder (20/7) = 6

Odd days in February = 0 (if non-leap year), 1 (if leap year)

Odd days in March = 3

Odd days in April = 2

Odd days in May = 3

Odd days in June = 2

So, number of odd days till June end in a non-leap year = 6 + 0 + 3 + 2 + 3 + 2 = 16 = 2

So, number of odd days till June end in a leap year = 6 + 1 + 3 + 2 + 3 + 2 = 17 = 3

July 12 means 11/7, i.e. 4 more odd days.

July 15 means 14/7, i.e. 0 more odd days.

So, day on July 12th (non-leap year): Sunday + 2 + 4 = Saturday

And, day on July 12th (leap year): Sunday + 3 + 4 = Sunday