Question 1

Calendar for the year 2008 will be the same for which of the following years?

Accepted Answer

Count the number of odd days from the year 2008 onward to get the sum equal to 0 odd day. Let us see 2008 = 2 2009 = 1 2010 = 1 2011 = 1 2012 = 2 2013 = 1 2014 = 1 2015 = 1 2016 = 2 2017 = 1 2018 = 1 Sum = 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 = 14 days = 2 weeks = 0 odd days ∴ Calendar for the year 2019 will be the same as for the year 2008

Question 2

At what time between 5 o'clock and 6 o'clock in the morning, will the both hands of a clock of a clock be at right angle?

Accepted Answer

Given that n = 5 and n + 1 = 6 The hands will make right angle at (5n ± 15) x 12/11 min past 5 . ⇒ (5 x 5 ± 15) x 12/11 min past 5. ⇒ (25 + 15) x 12/11 min past 5 and (25 - 15) x 12/11 min past 5. ⇒ 40 x 12/11 min past 5 and 10 x 12/11 min past 5. ⇒ 4801/11 min past 5 and 120/11 min past 5. ⇒ 437/11 min past 5 and 1010/11 min past 5.

Question 3

A watch which gains uniformly, is 5 min slow at 7 o'clock in the morning on Sunday and it is 5 min 48 s fast at 7 pm on following Sunday. Which day was it correct?

Accepted Answer

Time from 7 am on Sunday to 7 pm on following Sunday = 7 days 12 h = 180 h ∴ Watch gains (5 + 54/5) min or 54/5 in 180 h. Now, 54/5 min are gained in 180 h. ∴ 5 min gained in (180 x 5/54 x 5) h = 83 h 20 min. = 3 days 11 h and 20 min ∴ Watch is correct after 3 days 11 h and 20 min after 7 am of Sunday. ∴ It will be correct at 20 min past 6 pm on Wednesday.

Question 4

On the 6 March, 2005, Monday falls. What was the day of the week on 7th March 2004?

Accepted Answer

6th March 2005 = Monday. Then, 6th March 2004 = Monday - 1 day = Sunday [ ∵ 2004 is a leap year but it does not cross 29th February of 2004, so only 1 is taken as odd day. ] 6th March 2004 = Sunday 7th march 2004 = Monday.

Question 5

4th April, 1988 was Monday. What day of the week was it, on 6th November 1987?

Accepted Answer

Number of odd days between 6th November, 1987 and 4th April, 1988 . = (30 - 6) days of November 1987+ 31 days of December 1987 + 31 days of January 1988 + 29 days of February 1988 + 31 days March 1988 + 4 days of April 1988 = {(30 - 6 ) + 31 } + (31 + 29 + 31 + 4) = 24 + 31 + 31 + 29 + 31 + 4 = 150 = 21 weeks + 3 days = 3 odd days ∴ 6th November, 1987 will be three days backward from Monday. ∴ Required day is Friday.

Question 6

What was the day of the week on 17th July, 1776?

Accepted Answer

Period upto 17th July, 1776 = 1775 yr + Period from 1st January 1776 to 17th July 1776 Counting of odd days In 1600 yr = 0 In 100 yr = 5 75 yr = 18 leap years + 57 ordinary years = (18 x 2 + 57 x 1) odd days = 93 odd days = 13 weeks + 2 days = 2 odd days ∴ 1775 yr have(0 + 5 + 2) odd days = 7 odd days = 1 week + 0 odd day = 0 odd day Number of days between 1.1.1776 to 17.7.1776 January + February + March + April + May + June + July 31 + 29 + 31 + 30 + 31 + 30 + 17 = 199 days = 28 weeks + 3 odd days ∴ Total number of odd days = (3 + 0) = 3 Hence, the required day is Wednesday.

Question 7

What was the days of the week on 17th August , 2010?

Accepted Answer

Period up to 17th August, 2010 = (2009 yr + Period from 1.1.2010 to 17.8.2010) Counting of odd days Odd day in 1600 yr = 0 Odd days in 400 yr = 0 9 yr = (2 leap year + 7 ordinary years) = (2 x 2 + 7 x 1 ) = 1 Week + 4 days = 4 odd days Number of days between 1.1.2010 to 17.8.2010 January + February + March + April + May + June + July + August. = (31 + 28 + 31 + 30 + 31 + 30 + 31 + 17) days = 229 days = 32 weeks + 5 odd days Total number of odd days = (0 + 0 + 4 + 5) days = 9 days = 1 week + 2 odd days Hence, the required day is Tuesday.

Question 8

The last day of a century cannot be?

Accepted Answer

100 yr have 5 odd days. ∴ Last day of 1st century of is Friday. 200 yr have (5 x 2) = 1 week + 3 odd day = 3 odd day ∴ Last day of 2nd century of Wednesday, 300 yr have (5 x 3) = 2 week + 1 odd day = 1 odd day ∴ Last day of 3rd century is Monday. 400 yr have 0 odd day. ∴ Last day of 4th century is Sunday. This cycle is repeated. ∴ Last day of a century cannot be Tuesday of Thursday of Saturday.

Question 9

On what day dates March, 2005 did Saturday fall?

Accepted Answer

First, we find out the day on 1.03.2005. Period upto 1.3.2005. = (2004 yr + Period from 1.1.2005 to 1.3.2005) ∴ Odd day in 1600 yr = 0 Odd day in 400 yr = 0 4 yr = (1 leap year + 3 ordinary years) = (1 x 2 + 3 x 1) = 5 odd days Number of days between 1.1.2005 to 1.3.2005, = January + February + March = 31 + 28 + 1 = 60 days = (8 weeks + 4 days) = 4 odd days Total number of odd days = (0 + 0 + 5 + 4) = 9 = 1 weak + 2 odd days ∴ 1.3. 2005 was Tuesday. So, Saturday will fall on 5.3.2005. Hence, Saturday lies on 5th, 12th, 19th, and 26th of March 2005.

Question 10

What was the day of the week on 17th August, 2010?

Accepted Answer

Period upto 17th August, 2010 = (2009 yr + Period from 1.1.2010 to 17.8. 2010) Counting of odd days Odd day in 1600 yr = 0 Odd days in 400 yr = 0 9 yr = (2 leap years + 7 ordinary years) = ( 2 x 2 + 7 x 1) = 1 week + 4 days = 4 odd days Number of days between 1.1.2010 to 17.8.2010 January + February + March + April + May + June + July + August. = (31 + 28 + 31 + 30 + 31 + 30 + 31 + 17) days = 229 days = 32 weeks + 5 odd days Total number of odd days = (0 + 0 + 4 + 5 ) days = 9 days = 1 week + 2 odd days Hence, the required day is Tuesday.

Question 11

What was the day of the week on 5th June, 2002?

Accepted Answer

Period upto 5th June, 2002 = (2001 yr + Period from 1.1.2002 to 5.6.2002) ∴ Odd days in 1600 yr = 0 Odd days in 400 yr = 0 Odd days in 1 ordinary year = 1 Odd days in 2001 year = (0 + 0 + 1) = 1 Number of days from 1.1.2002 to 5.6.2002 January + February + March + April + May + June = 31 + 28 + 31 + 30 + 31 + 5 = 156 days = 22 weeks + 2 days = 2 odd days ∴ Total number of odd days = (1 + 2) = 3 ∴ The required day is Wednesday.

Question 12

Find at what time between 8 and 9 O'clock will the hands of a clock be in the same straight line but not together?

Accepted Answer

Question 13

Find the angle between the two hands of a clock at 30 minutes past 4 O'clock.

Accepted Answer

Question 14

My watch gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicates quarter past 4 O'clock, the true time is:

Accepted Answer

Question 15

A clock gains 10 minutes in every 24 hours. It is set right on Monday at 8 am. What will be the correct time on the following Wednesday, when the watch indicates 6 pm?

Accepted Answer

Question 16

A watch which gains uniformly is 6 minutes slow at 4 pm on a Sunday and 102/3 minutes fast on the following Sunday at 8 pm. During this period (Day and Time) when was the watch correct?

Accepted Answer

Question 17

India got independence on August 15, 1947. What was the day of the week?

Accepted Answer

As per the given above question , we know that August 15, 1947 = ( 1600 + 300 + 46 ) years + January 1 to August 15th, of 1947 August 15, 1947 = ( 1600 + 300 + 46 ) years + ( 365 - August 16 to December 31 1947 ) 1600 + 300 + 46 ) years August 15, 1947 = ( 1600 + 300 + 46 ) years + ( 365 - 138 ) days Now , 1600 years give 0 odd day 300 years give 1 odd day 46 years give 1 odd day Number of odd days = 0 + 1 + 1 (from 11 leap years and 35 ordinary years) + 3 = 5 odd days Hence , The day was Friday.

Question 18

January 7, 1992 was Tuesday. Find the day of the week on the same date after 5 years, i.e., on January 7, 1997?

Accepted Answer

We can say that , During the interval we have two leap years as 1992 and 1996 and it contains February of both these years. ∴ The interval has ( 5 + 2 ) = 7 days = 0 odd day. Hence, January 7, 1997 was also Tuesday.

Question 19

Calendar for 2000 will serve for also:

Accepted Answer

According to question , we know that Starting with 2000, count for number of odd days in successive years till the sum is divisible by 7. 2000 + 2001 + 2002 + 2003 + 2004 = 2 + 1 + 1 +1 + 2 = 7 odd days ∴ Number of odd days up to 2004 = 0 odd day Hence , Calendar for 2000 will serve for 2005 also.

Question 20

At what time are the hands of clocks together between 6 and 7?

Accepted Answer

Calendar Questions