Question

What will be the day of the week on 1st January, 2010?
A.Friday
B.Saturday
C.Sunday
D.Monday

Answer 1

Hint: Number of odd days in a year is 1 and the number of odd days in a leap year is 2. The number of days in a year is 365 days, where there is total number 52 weeks in a year where a week has 7 days so by (52 x 7=364 days) we can say a year has 1 extra day, while in a leap year there are 366 days so by (52 x 7=364 days) we can say a leap year has 2 odd days.
In this question first find the total number of odd days in the given year then we will find the day on that given date.

Complete step-by-step answer:
We are asked to find the day of the week on 1st January, 2010 so we will first find the number of odd days before 2010
Now since the year 2000 is a leap year so the number of odd days in 2000 \[ = 2days\]
Now consider the year 2001 since it is non-leap year so the number of odd days in 2001 \[ = 1day\]
Similarly year 2002 since it is non-leap year so the number of odd days in 2002 \[ = 1day\]
Also year 2003 is non-leap year so the number of odd days \[ = 1day\]
Now since the year 2004 is a leap year so the number of odd days\[ = 2days\]
Now again since 2005 is non-leap year so the number of odd days\[ = 1day\]
Similarly the year 2006 since it is non-leap year so the number of odd days\[ = 1day\]
Year 2007 a non-leap year so the number of odd day \[ = 1day\]
Now the year 2008 is a leap year so odd days\[ = 2days\]
Again since 2009 is non-leap year so the number of odd day\[ = 1day\]
So the total number of odd days from the year 2000 to 2009\[ = 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 = 13days\]
As we know 7 odd days makes a week hence we can number of odd days from the year 2000 to 2009\[ = 13 - 7 = 6days\]
Since 1st January, 2010 is non-leap year so number of odd days\[ = 1day\]
Hence the total number of odd days from the year 2000 to 2010\[ = 6 + 1 = 7days\]
And since 7 odd days makes a week so the number of odd days from the year 2000 to 2010\[ = 7 - 7 = 0\]
Therefore 1st January, 2010 will be Sunday.
So, the correct answer is “Option C”.

Note: Students can check whether a given year is a leap year or not by checking whether that year is divisible by 4 or not. In other words, if the year is completely divided by 4 then, it is leap year otherwise not.