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Question 1: If 15 March 1816 was Friday, what day of the week would 15th April 1916 be?
We are given that 15th March 1816 was a Friday.
Now we know that 100 years have 5 odd days. So till 15th March 1916, we will be having 5 odd days. So if we move from 15th March 1816 to 15th March 1916, we will encounter 5 odd days.
Now from 15th March 1916 to 15th April 1916 there would be 3 odd days.
So total number of odd days = 5+3 =8
8 mod 7 = 1
So 15th April 1916 would be Friday + 1= Saturday
Question 2: A leap year 1895 is having a same calendar as that of the year X. Which of the following is a possible value of X.
1895 is not a leap year. So it will have 1 odd day.
Since 1896 is a leap year, it will add 2 odd days.
Similarly 1987, 1898, 1899, 1900 will add 1,1,1,1 odd days.
Now the total number of odd days add up to 7.
So the next year 1901 will have the same calendar as 1895.
Question 3: If 28th August 1946 was a Wednesday, what day of the week was 31 August 1961?
It is given that 28th August 1946 was Wednesday. From 28th August 1946 to 28th August 1961, we have 4 leap years and 11 normal years. So the number of odd days would be
11*1 + 4*2 = 19
Now the date which is asked is 31 Aug 1961. So if we move from 28th August to 31st August, we will have 3 more odd days.
So total number of odd days = 5 + 3 = 8
Now 8 mod 7 = 1 .
So 31st August 1961 would be Wednesday + 1 = Thursday.
Question 4: If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a
30 years. The number of leap years is 8 (1972,1976,1980,1984,1988,1992,1996,2000).
So, the total number of days = 22*365 + 8*366 = 10958
10958 mod 7 = 3
Since 9/12/2001 is a Sunday, 9/12/1971 should be a Thursday.
Question 5: In 2016, Mohan celebrated his birthday on Friday. Which will be the first year after 2016 when Mohan will celebrate his birthday on a Wednesday? (He was not born in January or February)
Since it has been mentioned that Mohan was not born in February, so he can’t be born on 29th Feb. Hence He will celebrate his next birthday on a Wednesday in the year for which the sum of the odd days becomes 5 or a multiple of 5.
By his birthday in 2017, there will be 1 odd day.
By his birthday in 2018, there will be 2 odd days.
By his birthday in 2019, there will be 3 odd days.
By his birthday in 2020, there will be 5 odd days, as 2020 is a leap year.
So in 2020 He will celebrate his birthday on Wednesday.