If in a particular year 12th January is a Sunday, then which one of the following is correct?
  • a)
    15th July is a Sunday if the year is a leap year.
  • b)
    15th July is a Sunday if the year is not a leap year.
  • c)
    12th July is a Sunday if the year is a leap year.
  • d)
    12th July is not a Sunday if the year is a leap year.
Correct answer is option 'C'. Can you explain this answer?

UPSC Question

Balwant Singh
Mar 20, 2021
Case 1: if the year is a leap year
             (a) 15th July  =>     19(jan) + 29(feb) + 31(march) + 30(April) + 31(may) + 30(June) + 15(July)
    
                                           take modulus with 7 =>    (5 + 1 + 3 + 2 + 3 + 2 + 1 ) % 7 = 17 % 7 = 3    i.e.   sunday + 3days = Wednesday of 15july
            (b)   12 th july =>   (17 - 1 + 5) % 7 = 21 % 7 = 0   i.e.   sunday + 0 days = sunday on 12th july

similarly, we can calculate for case 2 i.e. not a leap year

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