During a particular year, exactly **ten** people ($A - J$) visited a certain city on five different days between **January 1st** and **April 30th**, in a non-leap year; such that on each of the five days, exactly **two** of the **ten** people visited the city.

It is also known that:

 1. $A$, who did not visit the city after $J$, visited the city $28$ days after $F$, who, in turn, did not visit the city with $B$.
 2. $J$, who visited the city in **March**, visited the city at least $50$ days
before $C$ visited but visited the city on the same day of the week as $C$.
 3. $D$, who visited the city exactly $10$ days before $H$, visited the city
with $G$.
 4. Both $E$ and $I$ visited the city on **February 10th**, while $E$ and $H$ visited the city on the same day of the week.

On which day did $B$ visit the city?
Source : time.com