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If the 1st day of a century is Friday then what could be the 1st day of the next century.
- a)Monday or Tuesday
- b)Sunday or Monday
- c)Tuesday or Wednesday
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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If the 1st day of a century is Friday then what could be the 1st day ...
In a period of 100 years there are 23 or 24 leap years (as for century year it might be or might not be a leap year, as 1900 was not a leap year)
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Number of odd days in a period of 100 years is 100 + 23 or 100 + 24 or 123/124 odd days.
Number of odd days in 100 years is when 123/124 is divided by 7, remainder is 4 or 5.
So next century should start with Monday or Tuesday.
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If the 1st day of a century is Friday then what could be the 1st day ...
Solution:
Given that the 1st day of a century is Friday.
Let us consider the first day of the 1st century as Friday.
We know that a century has 100 years.
Hence, the last year of the 1st century will be 100th year, which is the year 100.
We know that a year has 365 days (366 days for a leap year).
Hence, the 1st day of the 2nd century will be the 1st day of the year 101.
Now, we need to find out the 1st day of the 2nd century.
We can use the concept of odd days to find out the 1st day of any given year.
Odd days are the days left over after dividing the total number of days by 7.
For example, if we divide 365 days by 7, we get 52 weeks and 1 day left over. Hence, there is 1 odd day in 1 year.
Similarly, if we divide 366 days by 7, we get 52 weeks and 2 days left over. Hence, there are 2 odd days in 1 leap year.
Now, let us calculate the number of odd days in the 1st century.
We know that the 1st day of the 1st century is Friday.
Hence, the 1st day of the year 101 will be Saturday (1 odd day).
Similarly, the 1st day of the year 102 will be Sunday (2 odd days).
We can observe that for every 100 years, there are 5 odd days.
Hence, the 1st day of the 2nd century will be 5 days ahead of Friday, which is Wednesday (5 - 7 = -2, i.e. 2 days ahead of Friday).
Therefore, the possible options for the 1st day of the next century are Tuesday or Wednesday, which is option C.
Hence, the correct answer is option C.
Given that the 1st day of a century is Friday.
Let us consider the first day of the 1st century as Friday.
We know that a century has 100 years.
Hence, the last year of the 1st century will be 100th year, which is the year 100.
We know that a year has 365 days (366 days for a leap year).
Hence, the 1st day of the 2nd century will be the 1st day of the year 101.
Now, we need to find out the 1st day of the 2nd century.
We can use the concept of odd days to find out the 1st day of any given year.
Odd days are the days left over after dividing the total number of days by 7.
For example, if we divide 365 days by 7, we get 52 weeks and 1 day left over. Hence, there is 1 odd day in 1 year.
Similarly, if we divide 366 days by 7, we get 52 weeks and 2 days left over. Hence, there are 2 odd days in 1 leap year.
Now, let us calculate the number of odd days in the 1st century.
We know that the 1st day of the 1st century is Friday.
Hence, the 1st day of the year 101 will be Saturday (1 odd day).
Similarly, the 1st day of the year 102 will be Sunday (2 odd days).
We can observe that for every 100 years, there are 5 odd days.
Hence, the 1st day of the 2nd century will be 5 days ahead of Friday, which is Wednesday (5 - 7 = -2, i.e. 2 days ahead of Friday).
Therefore, the possible options for the 1st day of the next century are Tuesday or Wednesday, which is option C.
Hence, the correct answer is option C.
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