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QUESTION: 1

What was the day of the week on 16th August, 1947?

Solution:

15^{th} August, 1947 = (1946 years + Period from 1^{st} Jan., 1947 to 15th )

Counting of odd days:

1600 years have 0 odd day. 300 years have 1 odd day.

47 years = (11 leap years + 36 ordinary years)

= [(11 x 2) + (36 x 1) ] odd days

= 58 odd days

= 2 odd days

Jan Feb Mar Apr May Jun Jul Aug

= 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15

= 227 days

= (32 weeks + 3 days)

= 3,

Total number of odd days

= (0 + 1 + 2 + 3) odd days

= 6 odd days.

Hence, the required day was 'Saturday'.

QUESTION: 2

Prove that any date in March of a year is the same day of the week corresponding date in November that year.

Solution:

We will show that the number of odd days between last day of February and last day of October is zero.

March April May June July Aug. Sept. Oct.

31 + 30 + 31 + 30 + 31 + 31 + 30 + 31

= 241 days

= 35 weeks

= 0 odd day

Number of odd days during this period = 0.

Thus, 1^{st} March of an year will be the same day as 1^{st} November of that year. Hence, the result follows

QUESTION: 3

If today is Saturday, what will be the day 350 days from now ?

Solution:

350 days = (350/7 = 50 weeks) i.e No odd days,

So it will be a Saturday.

QUESTION: 4

The calendar for the year 1988 is same as which upcoming year ?

Solution:

We already know that the calendar after a leap year repeats again after 28 years.

Here 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.

QUESTION: 5

Given that on 9^{th} August 2016 is Saturday. What was the day on 9^{th} August 1616 ?

Solution:

We know that, After every 400 years, the same day occurs.

Thus, if 9^{th} August 2016 is Saturday, before 400 years

i.e., on 9^{th} August 1616 has to be Saturday.

QUESTION: 6

Second & fourth Saturdays and every Sunday is a holiday. How many working days will be there in a month of 31 days beginning on a Friday ?

Solution:

Given that the month begins on a Friday and has 31 days

Sundays = 3^{rd}, 10^{th}, 17^{th}, 24^{th}, 31^{st}

⇒ Total Sundays = 5

Every second & fourth Saturday is holiday. 2^{nd} & 4^{th} Saturday in every month = 2

Total days in the month = 31

Total working days = 31 - (5 + 2) = 24 days.

QUESTION: 7

On 17^{th} March, 1997 Monday falls. What day of the week was it on 17^{th} March, 1996?

Solution:

**Th**e year 1996 is a leap year. So, it has 2 odd days. But 17 th March comes after 29 th February. So, the day on 17 th March, 1997 will be 1 day beyond the day on 17 th March, 1996.

Here 17 th March, 1997 is Monday. So, 17 th March, 1996 is a **Sunday.**

QUESTION: 8

Which year has 366 days?

Solution:

When a century year leaves a remainder 0, when divided by 400 then it is a leap year (366 days).

So, 1200 has 366 days.

QUESTION: 9

What is 90 days from today?

(Hints : Today is 20th January 2017, Sunday)

Solution:

Given Today is 20^{th} January 2017, Sunday

In january, we have 31 days

February - 28 days (Non leap year)

March - 31 days

April - 30 days

⇒ Remaining days = 31 - 20 = 11 in Jan

11 in Jan + 28 in Feb + 31 in Mar = 11 + 28 + 31 = 70 days

More 20 days to complete 90 days ⇒ upto 20^{th} April

Therefore, after 90 days from today i.e, 20^{th} Jan 2017 is 20^{th} Apr 2017.

Now, the day of the week will be

90/7 ⇒ Remainder '6'

As the day starts with '0' on sunday

6 ⇒ Saturday.

Required day is 20^{th} April, Saturday.

QUESTION: 10

On 24th Nov, 2007 Thursday falls. What day of the week was it on 10th Nov, 2006 ?

Solution:

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 24^{th} Nov, 2007 will be 1 day beyond the day on 24

th Nov, 2006.

But, 24^{th} Nov, 2007 is Thursday.

24 - 10 = 14 days.

Therefore, 2 weeks ago it is same day.

Thus, 10^{th} Nov, 2006 is one day before 10^{th} Nov, 2007 i.e. it is Wednesday.

QUESTION: 11

The year next to 2003 will have the same calendar as that of the year 2003?

Solution:

Given year 2003, when divided by 4 leaves a remainder of 3.

NOTE: When remainder is 3, 11 is added to the given year to get the result.

So, 2003 + 11 = 2014

QUESTION: 12

On 19th June, 1984 Monday falls. What day of the week was it on 19th June, 1985?

Solution:

The year 1985 is an ordinary year. So, it has 1 odd day.

So, the day on 19th June, 1985 will be 1 day after the day on 19th June, 1984.

But, 19th June,1984 is Monday

So, 19th June, 1985 is Tuesday.

QUESTION: 13

Suppose today is Friday, what day of the week will it be 65 days from now?

Solution:

The day of the week repeats every 7 days.

Given today is Friday. Again Friday is repeated on the 7^{th} day, 14^{th},... on 7 multiple days.

Hence, Friday is on the 63^{rd} day, as 63 is multiple of 7.

Now, the required day of the week on the 65^{th} day is Sunday.

QUESTION: 14

How many seconds in 10 years?

Solution:

We know that,

1 year = 365 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds.

Then, 1 year = 365 x 24 x 60 x 60 seconds. = 8760 x 3600

1 year = 31536000 seconds.

Hence, 10 years = 31536000 x 10 = 315360000 seconds.

QUESTION: 15

The calendar of year 1939 is same as which year?

Solution:

Given year 1939, when divided by 4 leaves a remainder of 3.

**NOTE:** When remainder is 3, 11 is added to the given year to get the result.

So, 1939 + 11 = 1950

QUESTION: 16

What is two weeks from today?

Solution:

We know that the day repeats every 7 days, 14 days, 21 days, .........

So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday.

Hence, after 2 weeks i.e, 14 days the day repeats and is the same day.

QUESTION: 17

What will be your age in the year 2019 if you were born in 1995?

Solution:

Calculating Age has 2 conditions. Let your Birthday is on January 1^{st}.

1. If the month in which you are born is completed in the present year i.e, your birthday, then

Your Age = Present year - Year you are born

As of now, present year = 2018

i.e, Age = 2019 - 1995 = 24 years.

2. If the month in which you are born is not completed in the present year i.e, your birthday, then

Your Age = Last year - Year you are born

As of now, present year = 2019

i.e, Age = 2018 - 1995 = 23 years.

QUESTION: 18

What was the day on 2nd Jan 1901?

Solution:

2^{nd} Jan 1901 means

(1900 years and 2 day)

Now, 1600 years have 0 odd day

300 years have 1 odd day

2 days has 2 odd day

Total no. of odd days = 0 + 1 + 2 = 3 days

Hence, the day on 2^{nd} Jan 1901 was Wednesday.

QUESTION: 19

What was the day on 16th June,1993?

Solution:

16 June, 1993 = (1992 years + Period from 1.1.1993 to 16.6.1993)

Odd days in 1600 years = 0

Odd days in 300 years = 1

92 years = (69 ordinary years + 23 leap year) = (69 x 1 + 23 x 2)= 3 odd days

Jan. Feb. March April May June

(31 + 28 + 31 + 30 + 31 + 16 ) = 167 days

167 days = (23 weeks + 6 days) =6 odd days.

Total number of odd days = (0 + 1 + 3 + 6) = 3 odd days.

Given day is Wednesday.

QUESTION: 20

Which century year is a leap year?

Solution:

For an century year,it is divided by 400,when leaves a remainder 0 then it is a leap year. So, 1600

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