Calendars : 10 Expected Questions for the Exams

Ques 1.

Find the day of the week on 17th July, 1776.
Ans 1.
  17th July 1776 means : 1775 years + 6 months  + 17 days .
⇒   1600 years ( 400 x 4 years ) contain 0 odd days. 100 years contain 5 odd days.
⇒   75 years = 18 leap years  + 57 ordinary years = ( 18 x 2 ) + (57 x 1 ) odd days i.e. 93 odd days or 2 odd  days [ 93 - 7 gives 2 as remainder]
    ∴  1775 year contain  0 + 5+ 2  = 7 odd days i.e. 0 odd days
Number of days from jan. 1, 1776 to July 17, 1776 are:
⇒  31 + 29 + 31 + 30 + 31 + 17 = 199 days = 3 odd days [199- 7 gives  3 as remainder ]
  ∴ Total Number of odd days corresponding to the given date = 0 + 3 = 3 odd days.
⇒   Hence, the day on 17th July 1776 was Wednesday.

Ques 2.

What was the day on 10th November,1581 ?
Ans 2. 10th November,1581  means : 1580 years + 10 months + 10 days.
⇒  1200 years ( 400 x 3 years ) contain 0 odd days. 300 years contain 1 odd day.
⇒  80 years = 20 leap years  + 60 ordinary years  = ( 20 x 2) + 60 x 1) odd days i.e. 100 odd days or 2 odd days .
    ∴   1580 years contain 0 + 1 + 2 = 3 odd days.
Number of days from jan. 1, 1581 to Nov. 10, 1581 are:
⇒  31 + 28 + 31 + 30  + 31 + 30 + 31 + 31 + 30 + 31 + 10 = 314 days = 6 odd days.
  ∴   Total number of odd days corresponding  to the given date = 3 + 6 = 9 odd days i.e.2 odd days
⇒  Hence, the day on 10th November ,1581 was Tuesday.

Ques 3.

Today is Friday. What day will it be after 62 days ?
Ans 3. Each day to the week is repeated after 7 days.
  ∴    After 63 days ,it would be Friday.
⇒    So after 62 days, it would be Thursday.

Ques 4.

The First Republic Day of India was celebrate on 26th January . 1950.What was the day on that date?
Ans 4. 1600 years have 0 odd days.300 years have 1 odd day.
⇒    49 years contain 12 leap years and 37 ordinary years and therefore ( 24 + 37) odd days i.e. 5 odd days.
  ∴    1949 years contain (0 + 1 + 5) or 6 odd days.
⇒    26 days of January contain 5 odd days.
⇒    Total odd days = ( 6 + 5) = 11 or 4 odd days.
⇒    So the day was Thursday.

Ques 5.

Fine the calendar which is identical to the year 1998.
Ans 5.  We have to count the number of days from 1998 onwards  to get 0 odd days or the sum of the days divisible by 7.
                          Year  :    1998        1999         2000       2001      2002      2003    =  7 odd days
Number of odd days   :       1             1                2             1            1            1
     The year 2004 will have the same calendar as that of 1998.

Ques 6.

On 1st January ,1986 it was Wednesday.The day of the week on 1st january . 1987 was
(a) Tuesday
(b) Wednesday
(c) Thursday
(d) None of these
Ans 6. Thursday 
Hint : The year 1986 has one odd  day.


Ques 7.

If it was Saturday on December 17, 1982, what was the day on September 22, 1984 ?
(a) Sunday
(b) Monday
(c) Friday
(d) Saturday
Ans 7. Saturday 
Hint : Total number of  odd days between Sep. 22, 1984 and Dec. 17 ,1982 = 0 odd days 
Hence, Sep. 22, 1984  was also Saturday.


Ques 8.

It was Monday on 4th April, 1988.What was the day on 3rd November 1987?
(a) Monday
(b) Sunday
(c) Tuesday
(d) Wednesday
Ans 8.  Tuesday 
Hint : Total number of odd days between Nov. 3,1987 and Apr. 4, 1988 = 6 odd days. 
⇒    Let the  odd number associated with the day on 3rd Nov., 1987 be x. 
   ∴    x + 6 = 1   =>  x = 2  odd days  i.e. it was Tuesday .


Ques 9.

The day on 5th March of a year is the same day on which date of the same year ?
(a) 5th August
(b) 5th October
(c) 5th November
(d) 5th December
Ans 9.  5th November 
Hint : Take the given choices one by one .


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