Question

By using Zeller's formula, find the day for
a. 15/08/1947
b.26/01/1950

Answer 1

(a)  By Zeller's rule 15th of august,1947 was on a Friday.

(b) By Zeller's rule 26th of January,1950 was on a Thursday.

Step-by-step explanation:

Zeller's Rule:

$F=K+\frac{13\times m-1}{5}+D+\frac D4+\frac C4-2\times C$

F = No. of odd day

K = Date

m= Month (March is first and February is last month)

D= last two digit of year

C= First two digit of year.

If the given date has month January or February subtract 1 from the year.

(a)

15/08/1947

K= 15, m=08-2=6, D= 47 and C= 19

$F=K+\frac{13\times m-1}{5}+D+\frac D4+\frac C4-2\times C$

   $=15+\frac{13\times 6-1}{5}+47+\frac{47}{4}+\frac{19}{4}-2\times 19$

   =15+15+47+11+4-38     [ ignore decimal part]

   =54.

Now it is numerical value for the day, divide the number by 7. We need only reminder.

Here reminder is 5.

Reminder chat:

1= Monday

2= Tuesday

3= Wednesday

4= Thursday

5=Friday

6= Saturday

0= Sunday

Here 5 represents  Friday.

So, by Zeller's rule 15th of august,1947 was on a friday.

(b)

26/01/1950

For the 26 January 1950 subtract 1 from 1 i.e 1950-1=1949

K= 26, m=11, D= 50-1=49 and C= 19

$F=K+\frac{13\times m-1}{5}+D+\frac D4+\frac C4-2\times C$

   $=26+\frac{13\times 11-1}{5}+49+\frac{49}{4}+\frac{19}{4}-2\times 19$

   =26+28+49+12+4-38     [ ignore decimal part]

   =81

   =4

Here 3 represents  Thursday.

So, by Zeller's rule 26th of January,1950 was on a Thursday.

Answer 2

a. The day for 15/08/1947 is Friday.

b. The day for 26/01/1950 is Friday.

Step-by-step explanation:

The Zeller's formula is:

F = k + [(13 × m - 1)/5] + D + [D/4] + [C/4] - 2 × C

Where,

k = Day of the month

m = Month number

D = Last two digits of the year

C = First two digits of the year

a. 15/08/1947 :

F = 15 + [(13 × 6 - 1)/5] + 47 + [47/4] + [19/4] - (2 × 19)

F = 15 + 15.4 + 47 + 11.75 + 4.75 - 38

On discarding the decimals, we get,

F = 15 + 15 + 47 + 11 + 4 - 38

F = 54

F = 54 - 49 = 5

Thus, the day is Friday.

b. 26/01/1950:

F = 26 + [(13 × 11 - 1)/5] + 50 + [50/4] + [19/4] - (2 × 19)

F = 26 + 28.4 + 50 + 12.5 + 4.75 - 38

On discarding the decimals, we get,

F = 26 + 28 + 50 + 12 + 4 - 38

F = 82

F = 82 - 77 = 5

Thus, the day is Friday.