If the second Saturday and all Sundays are holidays in a $31\text{-day}$ month beginning on Friday, how many working days are there in that month?

The month has $31$ days and starts on a Friday (Day 1 = Friday).
Let's list the dates for Saturdays and Sundays:
Saturdays occur on:

* $1+1=2\text{nd}$ (First Saturday)
* $2+7=9\text{th}$ (Second Saturday - Holiday)
* $9+7=16\text{th}$
* $16+7=23\text{rd}$
* $23+7=30\text{th}$

Sundays occur on:

* $1+2=3\text{rd}$ (Holiday)
* $3+7=10\text{th}$ (Holiday)
* $10+7=17\text{th}$ (Holiday)
* $17+7=24\text{th}$ (Holiday)
* $24+7=31\text{st}$ (Holiday)

Total number of Sunday holidays = $5$
Total number of Saturday holidays = $1$ (only the second Saturday, which is on the $9\text{th}$)

Total holidays = $5+1=6$ days.

$$\text{Total Working Days}=\text{Total Days}-\text{Total Holidays}=31-6=25\text{ days}$$