Let $F$ denotes Facebook users,
$W$ denotes Whatsapp users ,
$F'$ denotes those not using Facebook, and
$W'$ denotes those not using Whatsapp.
$U$ denotes universal set.
Total faculties in institute, $n(U)=150$
Facebook users, $n(F)=55$
Whatsapp users, $n(W)=85$
Faculty members not using Facebook or Whatsapp $n(F' \cap W')=30$
Faculty members using either Facebook or Whatsapp
$n(F\cup W)= n(U)-n(F' \cap W') =150-30=120$
Faculty members using both Facebook and Whatsapp
$n(F \cap W) =n(F) +n(W) - n(F\cup W) = 55+85-120= 20$
Faculty members using Facebook only
$n(F \cap W')= n(F)-n(F \cap W)= 55 -20 =35$