How many days are there from 26th January 2008 to 15th May 2008, if both the starting day and the ending day are included in the count?

Introduction / Context:
This question asks for the number of calendar days between two specific dates in the year 2008, with the important detail that both the starting date and the ending date are to be included. Since 2008 is a leap year, February has 29 days, and this must be taken into account. The problem tests careful counting of days across multiple months and correct handling of inclusive ranges.

Given Data / Assumptions:

• Start date: 26th January 2008.
• End date: 15th May 2008.
• Both 26th January and 15th May are included in the count.
• Year 2008 is a leap year, so February has 29 days.

Concept / Approach:
The total number of days in an inclusive interval from date A to date B can be found by summing days in each month segment between the two dates, and adjusting for partial months at the beginning and end. For each complete month between the two endpoints, we add the full month length; for partial months, we count only the relevant days. Finally, we ensure that both the start and end dates are included in the total.

Step-by-Step Solution:
Step 1: In January 2008, count days from 26th to 31st inclusive. That gives 31 - 26 + 1 = 6 days. Step 2: February 2008 is in a leap year, so it has 29 days. All 29 are between the two dates, so we add 29. Step 3: March has 31 days. All 31 days fall within the interval, so add 31. Step 4: April has 30 days. All 30 days fall inside the range, so add 30. Step 5: In May, we count from 1st May to 15th May inclusive, which is 15 days. Step 6: Now sum all partial and full month contributions: 6 (January) + 29 (February) + 31 (March) + 30 (April) + 15 (May). Step 7: Compute 6 + 29 = 35; 35 + 31 = 66; 66 + 30 = 96; 96 + 15 = 111. Step 8: Therefore, there are 111 days from 26th January 2008 to 15th May 2008 inclusive.

Verification / Alternative check:
An equivalent method is to compute the serial day number of each date within the year and subtract. The day number of 26th January is 26. For 15th May, add full months before May: January 31, February 29, March 31, April 30, then plus 15 days of May. This sums to 31 + 29 + 31 + 30 + 15 = 136. Now the inclusive count between day 26 and day 136 is 136 - 26 + 1 = 111, which matches the previous calculation.

Why Other Options Are Wrong:
110, 112 and 113 would arise only if one of the months is miscounted, if February is treated as having 28 instead of 29 days, or if the inclusion of both endpoints is mishandled.

Common Pitfalls:
Students often forget that 2008 is a leap year and mistakenly use 28 days for February. Others may misapply inclusive counting and either omit the start day or the end day. Breaking the period month by month and using the simple formula last day minus first day plus one for partial months helps ensure accurate counting.

Final Answer:
There are 111 days between 26th January 2008 and 15th May 2008, including both dates.