Question

If Saturday falls on $4^{th}$ January 1997, what day of the week will fall on $4^{th}$ January 1998?

Answer 1

Hint: We know that the number of days in a year is 365 in a normal year and 366 in a leap year and the number of weeks in a year is 52. We also know that there are 7 days in a week. Thus, we will calculate how many days are accounted for the 52 weeks. If there are any remaining days, we will add that number of days in the week. For example, if we started counting from Monday and 2 days are left, we will go 2 days forward and the same date after 1 year will fall on Wednesday. Similarly, if we fall short of days for 52 weeks, we will go back in the week. If we start counting from Monday and we fall short of 2 days, the same date after 1 year will fall on Saturday.

Complete step-by-step solution:
As we know, there are 7 days a week and 52 weeks in a year.
Thus, the number of days in 52 weeks will be the product of 7 and 52.
$\Rightarrow $ Number of days in 52 weeks = 7 52.
$\Rightarrow $ Number of days in 52 weeks = 364
Thus, in 52 weeks, there are 364 days.
We know that the year 1997 is not a leap year, thus it will have 365 days.
So, the number of extra days is the difference between days in a year and the number of days in 52 weeks.
$\Rightarrow $ Extra days = $365 – 364 = 1$ day.
Thus, if we started counting from $4^{th}$ January 1997, which is a Saturday, after 52 weeks, the day will be Saturday and the date will be $3^{rd}$ January 1998.
Thus, Sunday will fall on $4^{th}$ January 1998.

Note: To identify whether the year is a leap year or not, we need to divide it by 4. If the year is divisible by 4, it is a leap year. Moreover, when the year is a century, it should be divisible by 400. For example, the year 1500 is divisible by 4, but it is not a leap year as it is not divisible by 400.