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 ?

The correct option is 22.

To find the minimum number of possible working days in any month of any year, we need to consider the month with the fewest total days and maximize the number of holidays in that month.

Step 1: Identify the month with the minimum total days.
February in a non-leap year has 28 days, which is the minimum number of days any month can have.

Step 2: Calculate the number of holidays in a 28-day month.
The given holidays are:
1. All Sundays
2. Second Saturday
3. Fourth Saturday

A month with 28 days consists of exactly 4 complete weeks (since 28 ÷ 7 = 4).
In 4 complete weeks, there are:
- Exactly 4 Sundays
- Exactly 4 Saturdays (which includes the 2nd Saturday and 4th Saturday)

Therefore, the total number of holidays in a 28-day month is:
$\text{Total Holidays}=4\text{(Sundays)}+1\text{(2nd Saturday)}+1\text{(4th Saturday)}=6\text{days}$

Step 3: Calculate the minimum working days.
Subtract the maximum possible holidays in a 28-day month from the total number of days in that month:
$\text{Minimum Working Days}=28-6=22\text{days}$

Thus, the minimum number of possible working days of any month of any year is 22.