Aptitude Calendar Sums with solutions

Introduction

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Formulas to use:

1. Odd Days:

We are supposed to find the day of the week on a given date. For this, we use the concept of 'odd days'. In a given period, the number of days more than the complete weeks are called odd days.

2. Leap Year:

(i) Every year divisible by 4 is a leap year, if it is not a century.

(ii) Every 4th century is a leap year and no other century is a leap year. Note: A leap year has 366 days.

Examples:

Each of the years 1948, 2004, 1676 etc. is a leap year.

Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.

None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

3. Ordinary Year:

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

4. Counting of Odd Days:

i) 1 ordinary year = 365 days = (52 weeks + 1 day.) 1 ordinary year has 1 odd day.

ii) 1 leap year = 366 days = (52 weeks + 2 days) 1 leap year has 2 odd days.

iii) 100 years = 76 ordinary years + 24 leap years.

= (76 * 1 + 24 * 2) odd days = 124 odd days.

= (17 weeks + days) = 5 odd days. Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) 3 odd days. Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 * 4 + 1) 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

5. Days of the week related to odd days

Sunday - 0

Monday - 1

Tuesday - 2

Wednesday - 3

Thursday - 4

Friday - 5

Saturday - 6

Solved Problems:

6. What was the day of the week on 28th May, 2006?

Answer: Sunday

Explanation:

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006) Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

Jan.31 + Feb.28 + March 31 + April 30 + May 28 = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7, so 0 odd day.

Given day is Sunday.

7. On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?

The year 2004 is a leap year. It has 2 odd days.

The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.

Hence, this day is Sunday.

8. What was the day of the week on 17th June, 1998?

Answer : Wednesday

Explanation :

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 * 3) = 1

97 years have 24 leap years + 73 ordinary years.

Number of odd days in 97 years (24 * 2 + 73) = 121 = 2 odd days.

Jan. Feb. March April May June

(31 + 28 + 31 + 30 + 31 + 17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

9. What will be the day of the week 15th August, 2010?

Answer : Sunday

Explanation :

15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 * 2 + 7 * 1) = 11 = 4 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 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.

Given day is sunday

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

Answer: Saturday

` Explanation:

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.

Conclusion

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