business mathematics

Important Facts and Formulae:

a) Odd Days : The number of days more than the complete number
of weeks in a given period is number of odd days during that
period.

b) Leap year : Every year which is divisible by 4 is called a
leap year. Thus each one of he year 1992,1996,2004,2008,..etc,
is a eap year.
Every 4th century is a leap year but no other century is a
leap year thus each one of 400,800,1200,1600,2000,etc is a
leap year. None of the 1900,2010,2020,2100,etc is a leap
year. An year which is not a leap year is called Ordinary year.

c)An ordinary year has 365 days.

d) A leap year has 366 days.

e)Counting of odd days :

i)1 ordinary year = 365 days =52 weeks+1 day,Therefore An
ordinary year has 1 Odd day.
ii)One leap year = 366 days =52 weeks+2 days, Therefore a leap
year has 2 Odd days.
iii) 100 years = 76 ordinary years+ 24 leap years
= [(76*52) weeks+76 days]+[(24*52)weeks+48 days]
= 5200 weeks+124days=[5217 weeks+5 days]
therefore 100 years contain 5 odd days
iv)200 years contain 10(1week+3days), i.e 3 odd days
v)300 years contain 15(2 weeks+1 day), i.e 1 odd day
vi)400 years contain (20+1), i.e 3 weeks,so 0 Odd days
similarly each one of 800,1200,1600,etc contains 0 odd days.

Note:(7n+m) odd days , where m less than or equal to 7
is equivalent to m odd days ,thus ,8 odd days = 1 odd day etc.

f) Some codes o remember the months and weeks:

a) Week

Sunday - 1
Monday - 2
Tuesday - 3
Wednesday - 4
Thursday - 5
Friday - 6
Saturday - 0

b) Month

jan - 1 july - 0
feb - 4 Aug - 3
Mar - 4 Sep - 6
Apr - 0 Oct - 1
May - 2 Nov - 4
june - 5 Dec - 6