#reasoningability

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Que 1: Find the Day on 14 September 1967?

Solution: 1967 is Non-Leap Year.

Step 1: As we know, there are zero odd days in every 400 years so the total number of odd days from 1 AD to 1600 AD = 0 ………..(i)

Step 2: Now there are 5 odd days in each century i.e. 17th, 18th and 19th century

Number of odd days= (5+5+5) mod 7= 1 …………(ii)

Step 3: Find the number of odd days from 1901 to 1966.

Number of leap years= 66/4= 16

Number of Non-Leap years= 66-16= 50

Number of Odd days= (16×2 +50×1) mod 7

=(2×2 +1×1) mod 7

=5 mod 7

=5 ……………(iii)

Step 4: Number of Odd days from January to August= (3+0+3+2+3+2+3+3) mod 7

=19 mod 7

=5 ……….(iv)

Number of Odd Days in next 14 days= 14 mod 7= 0 ……..(v)

Finally, the Total number of Odd Days= (0+1+5+5+0) mod 7

=11 mod 7

=4 

Here, 4 represents Thursday.

Que 2: Find the Day on 25 April 1868?

Solution: 1868 is a Leap Year (there would be 29 days in February)

Step 1: Odd Days=0

Step 2: Odd Days in 17th and 18th Century= (5+5) mod 7=3 

Step 3: Odd Days from 1801 to 1867

Number of leap years= 67/4= 16

Non-Leap years= 67-16=51

Odd Days=(16×2 +51×1) mod 7 

=(2×2 +2×1) mod 7

=6 mod 7

=6

Step 4: Odd days in the rest of the days=(3+1+3+25) mod 7

=(7+4) mod 7

=11 mod 7

=4

Total number of Odd Days=(0+3+6+4) mod 7

=13 mod 7

=6