Question:medium

If Second Saturday and Sunday of every month is a holiday, then the total number of working days in a month of 31 days beginning with a Wednesday will be

Updated On: Jul 15, 2026
  • 23
  • 24
  • 25
  • 26
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The Correct Option is D

Approach Solution - 1

Step 1: Understanding the Question.
The month has 31 days and starts on a Wednesday. Every Sunday is a holiday, and the second Saturday of the month is also a holiday. We need the count of working days.

Step 2: Key Formula or Approach.
31 days breaks into 4 complete weeks (28 days) plus 3 extra days. Each complete week has exactly 1 Sunday, so we get 4 Sundays from the 4 weeks, and we then add the second Saturday as one more holiday.

Step 3: Detailed Explanation.
Day 1 of the month is Wednesday, so day 28 (4 weeks later) is also a Wednesday, and the leftover days 29, 30, 31 are Thursday, Friday, Saturday.
The first Sunday falls on day 5 (since Wednesday, Thursday, Friday, Saturday, Sunday are days 1 to 5).
Sundays therefore fall on days 5, 12, 19 and 26, that is 4 Sundays within the 31 days.
The Saturdays fall on days 4, 11, 18 and 25, so the second Saturday is day 11, which is not already one of the Sunday dates.
Total holidays = 4 Sundays + 1 second Saturday = 5.
\[ \text{Working days} = 31 - 5 = 26 \]

Step 4: Final Answer.
There are 26 working days in the month. \[ \boxed{26} \]
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Approach Solution -2

We can also count the holidays by looking at how often each weekday repeats across the 31 days. Since \( 31 = 4 \times 7 + 3 \), the month contains 4 complete weeks plus 3 extra days. In any such month, the weekdays that fall on the first 3 days of the month occur 5 times each, while every other weekday occurs exactly 4 times. Day 1 is a Wednesday, so days 2 and 3 are Thursday and Friday, meaning Wednesday, Thursday and Friday each occur 5 times, and all other weekdays, including Saturday and Sunday, occur exactly 4 times. So there are exactly 4 Sundays. For the Saturdays, since day 1 is Wednesday, the first Saturday is day 4, so the four Saturdays fall on days 4, 11, 18 and 25, making the second Saturday day 11. Total holidays = 4 Sundays + 1 second Saturday = 5. Let's test each option against this.

  1. Option (A): 23: This needs 8 holidays, which would require Sunday to be one of the 3 weekdays that repeat 5 times in this calendar, but Sunday falls outside the Wednesday-Thursday-Friday group that repeats 5 times, so 8 holidays cannot occur.
  2. Option (B): 24: This needs 7 holidays, again more than the 4 Sundays the frequency count allows for, so this does not fit either.
  3. Option (C): 25: This needs 6 holidays, one more than the 5 that the frequency count and the single second-Saturday rule actually produce.
  4. Option (D): 26: This matches \( 31 - 5 = 26 \), using the 4 Sundays (from the 4-times weekday group) plus the single second Saturday identified at day 11.

Counting which weekdays repeat 5 times versus 4 times in this 31-day month confirms 4 Sundays and 1 second Saturday, 5 holidays, and 26 working days.

Therefore, the correct answer is 26.

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