Question:
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
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
The correct option is (D): 26.
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Approach Solution -2
We need the number of working days in a 31-day month that starts on a Wednesday, where every Sunday and the second Saturday of the month are holidays. Let's list out the calendar day by day and count the holidays directly, then check which option matches.
- Option (A): 23: This would mean 8 holidays in the month. Listing the days from Wednesday (day 1) onward, the Sundays fall on days 5, 12, 19 and 26, which is 4 Sundays, and the second Saturday falls on day 11, giving 5 holidays in total, not 8. So 23 is too low.
- Option (B): 24: This would need 7 holidays, still more than the 5 holidays actually present in the calendar (4 Sundays plus 1 second Saturday), so this does not match either.
- Option (C): 25: This would need exactly 6 holidays. The calendar only gives 5 holidays (days 5, 11, 12, 19, 26), so 25 is one day short of correct.
- Option (D): 26: With 4 Sundays (days 5, 12, 19, 26) and 1 second Saturday (day 11) as holidays, that is 5 holidays out of 31 days, leaving 31 minus 5 equals 26 working days. This matches the calendar exactly.
Counting the actual calendar confirms there are 5 holidays and 26 working days.
Therefore, the correct answer is 26.
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The month has 31 days and day 1 falls on a Wednesday. We can assign each day a position in the week using modular arithmetic: counting Wednesday as position 0, Thursday as 1, Friday as 2, Saturday as 3, Sunday as 4, Monday as 5, and Tuesday as 6, the weekday of day \( n \) is given by \( (n - 1) \bmod 7 \). A day is a Sunday when \( (n - 1) \bmod 7 = 4 \), which happens at \( n = 5, 12, 19, 26 \), so there are exactly 4 Sundays. A day is a Saturday when \( (n - 1) \bmod 7 = 3 \), which happens at \( n = 4, 11, 18, 25 \), so the second Saturday falls on \( n = 11 \). That gives \( 4 + 1 = 5 \) holidays, so working days = \( 31 - 5 = 26 \). Let's check each option against this count.
- Option (A): 23: This would require 8 holidays in the month, but the congruence \( (n-1) \bmod 7 = 4 \) only has 4 solutions in the range 1 to 31, and only one date satisfies the second-Saturday condition, so 8 holidays is not possible under this calendar.
- Option (B): 24: This would require 7 holidays, still more than the 5 dates that actually satisfy the Sunday and second-Saturday congruences worked out above.
- Option (C): 25: This would require exactly 6 holidays, one more than the 5 values \( n = 5, 11, 12, 19, 26 \) that the congruences actually produce, so this overcounts by one holiday that does not exist.
- Option (D): 26: This matches \( 31 - 5 = 26 \) exactly, using the 5 holiday dates \( n = 5, 11, 12, 19, 26 \) obtained directly from the two modular conditions.
Solving the weekday congruences directly gives exactly 4 Sundays and 1 second Saturday, 5 holidays in total, leaving 26 working days.
Therefore, the correct answer is 26.
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