Mohan correctly remembers that his father's birthday is before $20^{th}$ January but after $16^{th}$ January,whereas his sister correctly remembers that their father's birthday is after $18^{th}$ January but before $23^{rd}$ January. On which date in January is their father's birthday?

• A
  $18^{th}$
• B
  $19^{th}$
• C
  $20^{th}$
• D
  Data inadequate