In a company, all Mondays and Sundays are official holidays. If a certain month with 31 days starts on a Monday, how many total holidays (offs) will occur in that month?

Introduction / Context:
This question tests your ability to interpret a simple calendar scenario where certain days of the week are fixed as holidays. You must count how many Mondays and Sundays occur in a 31 day month that starts on a Monday. Such counting questions are straightforward but require systematic thinking to avoid mistakes, especially in competitive exams where small slips can cost marks.

Given Data / Assumptions:

• The month has 31 days.
• The first day of the month is a Monday.
• All Mondays and all Sundays in that month are holidays.
• We assume a standard seven day week, repeating Monday through Sunday.

Concept / Approach:
The easiest way to solve this is to list or visualise the weekdays for key dates in the month. Since 31 days cover exactly four full weeks (28 days) plus three extra days, the pattern of weekdays will repeat every seven days. We specifically need to count how many occurrences of Monday and Sunday fall within the 31 day range. Once we know how many Mondays and how many Sundays occur, we simply add them to get the total number of holidays.

Step-by-Step Solution:
Step 1: Place day 1 of the month on Monday, as given. Step 2: Because weekdays repeat every 7 days, Mondays will fall on days 1, 8, 15, 22, and 29. Step 3: This gives us 5 Mondays in the month. Step 4: The first Sunday will be 6 days after Monday, so Sundays fall on days 7, 14, 21, and 28. Step 5: This gives us 4 Sundays in the month. Step 6: There are no additional Mondays or Sundays beyond day 29 and day 28 respectively, because the month ends on day 31 which is a Wednesday. Step 7: Total holidays are Mondays plus Sundays, so total holidays = 5 + 4 = 9.

Verification / Alternative check:
You can quickly sketch a mini calendar: write days 1 to 31 in rows of seven, starting with Monday. You will see that the fifth Monday appears on the 29th, and that Sundays appear four times within the first 28 days. Another quick check is to remember that in a 31 day month starting on Monday, the sequence of weekdays for the dates 29, 30, and 31 will be Monday, Tuesday, and Wednesday. This confirms that no extra Sunday sneaks in at the end of the month, and that Mondays total five while Sundays total four.

Why Other Options Are Wrong:
An answer of 7 or 8 usually comes from forgetting either the fourth Sunday or the fifth Monday. An answer of 5 is clearly too low, because there are already four Sundays alone. None of these match the correct combined count of all Mondays and Sundays in the month. Only 9 is consistent with the structured counting of weekdays across the 31 days.

Common Pitfalls:
Students sometimes miscount by trying to count every day mentally instead of using the 7 day cyclic pattern. Others count Mondays correctly but overlook that there are four Sundays, or vice versa. Another frequent mistake is thinking that there must be the same number of Mondays and Sundays, which is not true when the month length is 31 days and starts on a Monday. Always rely on the seven day cycle and list critical dates such as 1, 7, 8, 14, 15, 21, 22, 28, and 29 to avoid confusion.

Final Answer:
Thus, the total number of holidays (Mondays and Sundays) in such a month is 9.