Question 1

In a month of 31 days, third Thursday falls on 16th. What will be the last day of the month?

Accepted Answer

Friday will fall on 3, 10, 17, 24, 31 So, it will be 5th Friday on 31 st

Question 2

How many times in a day (24 Hrs), are the hands of a clock in straight line but opposite in direction?

Accepted Answer

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite direction at 6 'o clock only). So, in a day, the hands point in the opposite direction 22 times.

Question 3

On what dates of April, 2001 did Friday fall?

Accepted Answer

Lets find out 1st April from Zeller's Formula: f = k + [13 x m - 1 / 5] + D + [D/4] + [C/4] - 2 x C. In this case k = 1 (since 1st April) Month m = 2 (As march = 1, April = 2) D is the last two digit of year here D = 01 (As year is 2001) C is 1st two digit of century here C = 20 (As year is 2001) f = 1 + [13 x 2 - 1 / 5] + 01 +[01/4] + [20/4] -2 x 20 f = 1 + [25/5] + 01 + [0.5] + [5] - 40. f = 1 + 5 + 01 + 0 + 5 - 40 = -28 This - ve value of f can be made positive by adding multiple of 7 So f = - 28 + 28 = 0 So number of odd days is 0, So 1st April 2001 is Sunday, So 1st Friday is on 6th April , so next Fridays is 13th, 20th, 27th April.

Question 4

How many Sundays will be in a period of 100 years.

Accepted Answer

In a period of 100 years there are 23 or 24 leap years (as for century year it might be or might not be a leap year, as 1900 was not a leap year) Number of days in a period of 100 years is 365 x 100 + 23 or 365 x 100 + 24. If century year is not a leap year then number of days = 365 x 100 + 23, and number of weeks is 5217 and 4 odd and for leap year it will be 5217 weeks and 5 odd days, hence number of Sundays is either 5217 or 5218.

Question 5

Calendar of which one of the following 2 years is similar?

Accepted Answer

Calendar of 2 years is similar if number of odd days between these two years is zero. Consider option one by one (a) Between 1940 to 1946 we have two leap years 1940 and 1944 so number of odd days is 2 + 1 + 1 + 1 + 2 + 1 = 8 or 1 hence calendar of these two years is not similar. (b) Between 1977 to 1982 we have one leap years 1980 so number of odd days is 1 + 1 + 1 + 1 + 2 + 1 = 6 calendar of these two years is not similar. (c) Between 1912 to 1916 we have one leap years 1912 so number of odd days is 2 + 1 + 1 + 1 = 5 hence calendar of these two years is not similar.

Question 6

Calendar of 2013 is related to calendar of 2015 same as calendar of 1977 to which one of the following year?

Accepted Answer

Number of odd days between 2013 and 2015 is 2, so we have to find the year which will have 2 odd days between 1977 and required year. Consider options one by one - (a) Number of odd days between 1977 and 1981 is 1 + 1 + 1 + 2 = 5 odd days (b) Number of odd days between 1977 and 1985 is 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 = 10 odd days or 3 odd days (c) Number of odd days between 1977 and 1990 is 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 = 16 odd days or 2 odd days, hence calendar of 1990 is the answer.

Question 7

Which of the following year has 53 Sundays?

Accepted Answer

In a year we have 53 Sundays only when year start with Sunday (For non leap year) and either with Saturday of Sunday (For leap year). From zeller's formula 1st January 2001 was Monday From number of odd days 1st January 2006 will start with Sunday so it had 53 Sunday Similar 1stJanuary 2009 will start with Thursday.

Question 8

If in a particular year 'X' there are 53 Sundays then how many Sundays will be there in a period of four years X to X + 3 year.

Accepted Answer

Let us take two cases Case (i) : When year start with Sunday then next 4 years will always have 52 Sundays hence total number of Sundays are 53 + 3 x 52 = 209 Sundays Case (ii) : When year start with Sunday and then we have 53 Sundays that means year is a leap year then next 4 years will always have 52 Sundays hence total number of Sundays are 53 + 3 x 52 = 209 Sundays.

Question 9

If in a particular month there are 5 Thursday then how many Fridays are there in next month.

Accepted Answer

If month ends with Thursday then next month will start with Friday and it may have 5 Friday otherwise it may have 4 Fridays.

Question 10

Mondays falls on 20th March, 1995. What was the day on 3rd November, 1994?

Accepted Answer

Counting the number of days after 3rd November. 1994 we have : Number of Days in November = 27 or 6 odd days. Number of Days in December = 31 or 3 odd days. Number of Days in January = 31 or 3 odd days. Number of Days in February = 28 or 0 odd days. Number of Days in March = 20 or 6 odd days. So total number of odd days = 6 + 3 + 3 + 0 + 6 = 18 when divided by 7 gives remainder 4. Number of odd days = 4 The day on 3rd November, 1994 is (7 - 4) days beyond the day on 20th March, 1995. So, the required day is Thursday.

Question 11

If 94 days back it was Monday then after how many days we will get a Sunday?

Accepted Answer

94 when divided by 7 gives remainder 3 hence today it must be Thursday, after 3 more we will get a Sunday, next Sunday will be after 3 + 7 = 10 days and so on so we will get Sunday after a day 7K + 3 days.

Question 12

The last day of century can be which of the following day?

Accepted Answer

100 years contain 5 odd days. ∴ Last day of 1st century is Friday. 200 years contain (5 x 2) = 3 odd days. ∴ Last day of 2nd century is Wednesday. 300 years contain ( 5 x 3) = 15 = 1 odd day. ∴ Last day of 3rd century is Monday 400 years contain 0 odd day. ∴ Last day of 4rd century is Sunday. This cycle is repeated that means last day of century is Friday, Wednesday, Monday, or Sunday and it repeats the cycle.

Question 13

If in a year December has 9 weekends (Saturday and Sunday) then in that year January had how many weekends?

Accepted Answer

Here we have two cases : Case (i) : If a month start with Thursday the month will have 5 Saturdays and 4 Sundays i.e total 9 weekends. In this case 31st December will be Sunday hence 1st January will be either Sunday (For non leap year) or Saturday ( For leap year) then January will have 9 or 10 weekends. Case (ii) : If a month start with Sunday the month will have 4 Saturdays and 5 Sundays i.e total 9 weekends. In this case 31st December will be Wednesday hence 1st January will be either Wednesday (For non leap year) or Tuesday ( For leap year) then January will have 8 or 9 weekends. Hence number of weekends in January will be 8 or 9 or 10.

Question 14

If in a particular year there are 53 weekends (i.e Saturday and Sunday) then how many weekends January of that year has.

Accepted Answer

If there are 53 Saturday and Sunday that means year is a leap year and last day of year and last day of year is Sunday so 1st day of January must be Saturday then January will have 10 weekends.

Question 15

If 1 st day of a century is Thursday then what could be the 1 st day of next century.

Accepted Answer

In a period of 100 years there are 23 or 24 leap years (as for century year it might be or might not be a leap leap year, as 1900 was not a leap year) Number of odd days in a period of 100 years is 100 + 23 or 100 + 24 or 123/124 odd days. Number of odd days in 100 years is when 123/124 divided by 7, remainder is 4 or 5. So next century should start with Monday or Tuesday.

Question 16

If 1 st January of a particular year (say x) is Monday then what will be the 1 st day of the year 100 years after (i.e year x + 100).

Accepted Answer

In a period of 100 years there are 23 or 24 leap (as for century year it might be or might not be a leap leap year, as 1900 was not a leap year) Number of odd days in a period of 100 years is 100 + 23 or 100 + 24 or 123/124 odd days. Number of odd days in 100 years is when 123/124 divided by 7, remainder is 4 or 5. So next century should start with Friday or Saturday.

Question 17

1 st day of century can not start with which of the following day?

Accepted Answer

Last day of century can be Friday, Wednesday, Monday, or Sunday and it repeats the cycle. So 1st day of next century must be either Saturday, Thursday, Tuesday, or Monday and so it must not be Wednesday, friday & Sunday

Question 18

Calendar of month July is same as that of which month of previous year.

Accepted Answer

If previous year is leap year then calendar of May is similar to July

Question 19

What was the day on 15th august 1947 ?

Accepted Answer

To find the day of the week for any given date, we can use a formula called Zeller's Congruence. Here are the steps: Write down the date: 15th August 1947. Day (q) = 15 Month (m) = 8 (August) Year = 1947, so we get: K = 47 (last two digits of the year) J = 19 (first two digits of the year) Apply the formula: The formula for Zeller's Congruence is: h = (q + floor(13(m + 1) / 5) + K + floor(K / 4) + floor(J / 4) - 2J) mod 7 Plug the values into the formula: h = (15 + floor(13(8 + 1) / 5) + 47 + floor(47 / 4) + floor(19 / 4) - 2(19)) mod 7 Calculate the terms: floor(13(9) / 5) = floor(117 / 5) = 23 floor(47 / 4) = 11 floor(19 / 4) = 4 Final calculation: h = (15 + 23 + 47 + 11 + 4 - 38) mod 7 Simplified: h = 62 mod 7 = 6 Interpret the result: h = 6, which corresponds to Friday (where 0 = Saturday, 1 = Sunday, ..., 6 = Friday). Thus, 15th August 1947 was a Friday.

Question 20

Today is Monday. After 61 days, it will be :

Accepted Answer

Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday.

Calendar Questions