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)

• A month has a minimum of 28 days, which consists of exactly 4 weeks, meaning there are always 4 Sundays in any month.

• To minimize working days, we must maximize the number of holidays. The holidays are all Sundays plus the 2nd and 4th Saturdays.

• In a 28-day month, there are exactly 4 Saturdays. The 2nd and 4th Saturdays are distinct days and are always present.

• Therefore, the total number of holidays in the minimum case is 4 Sundays + 2 Saturdays = 6 holidays.

• The minimum number of working days is calculated as Total Days (28) - Total Holidays (6) = 22.

Why the other options are wrong

(a) 23: Option (a) is incorrect because 23 working days would imply only 5 holidays, which is less than the guaranteed 6 holidays (4 Sundays + 2 specific Saturdays) in a 28-day month.
(c) 21: Option (c) is incorrect because 21 working days would imply 7 holidays, which is impossible in a 28-day month as there are only 4 Sundays and only 2 of the 4 Saturdays are holidays.
(d) 20: Option (c) is incorrect because 20 working days would imply 8 holidays, which exceeds the maximum possible holidays (6) in a 28-day month.

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.