The calendar for 1990 is the same as for A. 1992 B. 1995 C. 1996 D. 2001 Answer Workspace Report Discuss Answer with explanation Answer: Option D Explanation For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0. Take the year 1992 from the given choices. Total odd days in the period 1990-1991= 2 normal years ≡ 2 x 1 = 2 odd days Take the year 1995 from the given choices. Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year ≡ 4 x 1 + 1 x 2 = 6 odd days Take the year 1996 from the given choices. Number of odd days in the period 1990-1995= 5 normal years + 1 leap year ≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days As we can reduce multiples of 7 from odd days which will not change anything Though number of odd days in the period 1990-1995 is 0, there is a catch here. 1990 is not a leap year whereas 1996 is a leap year. Hence calendar for 1990 and 1996 will never be the same. Take the year 2001 from the given choices. Number of odd days in the period 1990-2000= 8 normal years + 3 leap years ≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days Also, both 1990 and 2001 are normal years. Hence 1990 will have the same calendar as that of 2001 Workspace

sravani eda says September 18, 2019 at 11:28 am Repetition of leap year ===> Add +28 to the Given Year. Repetition of non leap year Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2. Step 2: Add +6 to the Given Year. Solution : Given Year is 2024, Which is a leap year. So, Add +28 to the given year (i.e 2024 + 28) = 2052 Therfore, The calendar of the year 2024 can be used again in the year 2052. Reply

Srinu says March 18, 2020 at 12:01 pm how can 1990( a non leap year) and 1996( a leap year) be the same? Reply

Vamsi says March 19, 2020 at 11:14 am For a year to have the same calendar with 1990, the total odd days from 1990 should be 0. Take the year 1992 from the given choices. Total odd days in the period 1990-1991= 2 normal years ≡ 2 x 1 = 2 odd days Take the year 1995 from the given choices. Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year ≡ 4 x 1 + 1 x 2 = 6 odd days Take the year 1996 from the given choices. Number of odd days in the period 1990-1995= 5 normal years + 1 leap year ≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days As we can reduce multiples of 7 from odd days which will not change anything Though number of odd days in the period 1990-1995 is 0, there is a catch here. 1990 is not a leap year whereas 1996 is a leap year. Hence calendar for 1990 and 1996 will never be the same. Take the year 2001 from the given choices. Number of odd days in the period 1990-2000= 8 normal years + 3 leap years ≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days Also, both 1990 and 2001 are normal years. Hence 1990 will have the same calendar as that of 2001 Reply

Ajay says

why??

sravani eda says

Repetition of leap year ===> Add +28 to the Given Year.

Repetition of non leap year

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2: Add +6 to the Given Year.

Solution :

Given Year is 2024, Which is a leap year.

So, Add +28 to the given year (i.e 2024 + 28) = 2052

Therfore, The calendar of the year 2024 can be used again in the year 2052.

Srinu says

how can 1990( a non leap year) and 1996( a leap year) be the same?

Vamsi says

For a year to have the same calendar with 1990, the total odd days from 1990 should be 0.

Take the year 1992 from the given choices.

Total odd days in the period 1990-1991= 2 normal years

≡ 2 x 1 = 2 odd days

Take the year 1995 from the given choices.

Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year

≡ 4 x 1 + 1 x 2 = 6 odd days

Take the year 1996 from the given choices.

Number of odd days in the period 1990-1995= 5 normal years + 1 leap year

≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days

As we can reduce multiples of 7 from odd days which will not change anything

Though number of odd days in the period 1990-1995 is 0, there is a catch here.

1990 is not a leap year whereas 1996 is a leap year.

Hence calendar for 1990 and 1996 will never be the same.

Take the year 2001 from the given choices.

Number of odd days in the period 1990-2000= 8 normal years + 3 leap years

≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days

Also, both 1990 and 2001 are normal years.

Hence 1990 will have the same calendar as that of 2001