## 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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