This question asks us to determine the day of the week for a future date based on a known past date. We are given that 18^th February, 2005, was a Friday, and we need to find the day for 18^th February, 2007.

Calculating the Day Shift Between Dates

To find the day of the week for the later date, we need to calculate the total number of days between the two given dates (18^th February, 2005 and 18^th February, 2007) and then determine the number of 'odd days'. An odd day is the remainder left after dividing the total number of days by 7.

Number of Years and Odd Days

The time span is from 18^th February, 2005, to 18^th February, 2007. This covers exactly 2 years.

• Year 1: 18^th February, 2005 to 17^th February, 2006
• Year 2: 18^th February, 2006 to 17^th February, 2007

We need to check if any leap years occur within this period. A leap year has 366 days, while a normal year has 365 days. A year is typically a leap year if it is divisible by 4.

• The year 2005 is not divisible by 4, so it is a normal year.
• The year 2006 is not divisible by 4, so it is a normal year.
• The year 2007 is not divisible by 4, so it is a normal year.

The period from 18^th February, 2005, to 18^th February, 2007, does not include a February 29^th. Therefore, both years in this span can be treated as normal years regarding the day calculation.

Calculating Total Odd Days

A normal year has 365 days. To find the odd days in a normal year, we calculate the remainder when 365 is divided by 7:

$$ \text{Number of odd days} = \frac{365}{7} $$

$$ 365 = (52 \times 7) + 1 $$

So, a normal year has 1 odd day.

Since we have two normal years between 18^th February, 2005, and 18^th February, 2007:

• Odd days from 18^th Feb 2005 to 18^th Feb 2006 = 1 odd day.
• Odd days from 18^th Feb 2006 to 18^th Feb 2007 = 1 odd day.

Total odd days = 1 + 1 = 2 odd days.

Determining the Final Day

We are given that 18^th February, 2005, was a Friday. To find the day on 18^th February, 2007, we add the total number of odd days (2) to the starting day (Friday).

• Friday + 1 day = Saturday
• Saturday + 1 day = Sunday

Therefore, 18^th February, 2007, will fall on a Sunday.

Summary Table