If second and fourth Saturdays and all the Sundays are taken as only holidays for an office, what would be the minimum number of possible working days of any month of any year?
- (a) 23
- (b) 22 ✓ UPSC's answer
- (c) 21
- (d) 20
Why the answer is (b)
• Every month has at least 28 days, which guarantees at least 4 Saturdays and 4 Sundays, so the 2nd and 4th Saturdays always exist as holidays regardless of the month's length or starting day.
• The total number of holidays in a month equals 2 (the 2nd and 4th Saturdays) plus the number of Sundays in that month, since a Saturday can never coincide with a Sunday.
• A 28-day month contains exactly 4 of each weekday, giving 4 Sundays and 2 Saturday-holidays for a total of 6 holidays, leaving 28 − 6 = 22 working days.
• A 29-day month (February in a leap year) can contain 5 Sundays if it begins on a Sunday, giving 5 + 2 = 7 holidays and 29 − 7 = 22 working days; no shorter month exists, so 22 is the floor.
• Longer months (30 or 31 days) can also reach 7 holidays, but the extra days push working days to 23 or 24, so they cannot beat the 22-day result.
• The minimum possible number of working days in any month of any year is therefore 22, so the answer is option (b).
Why the other options are wrong
- (a) 23
- 23 working days would correspond to a 30-day month with 7 holidays (5 Sundays + 2 Saturdays) or a 29-day month with only 4 Sundays; it is not the minimum because a 28-day month already yields 22 working days.
- (c) 21
- 21 working days would require 7 holidays in a 28-day month, but a 28-day month has exactly 4 of each weekday, so it can have at most 4 Sundays plus 2 Saturday-holidays = 6 holidays, giving 22 working days at best.
- (d) 20
- 20 working days would require 8 holidays in a 28-day month or 9 in a 29-day month, which is impossible since the maximum number of Sundays in any month is 5 and only 2 Saturdays are holidays, capping total holidays at 7.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.