Before the merger:
$X$ Ltd. had no. of employees =4
$Y$ Ltd. had no. of employees =3
$Z$ Ltd. had no. of employees =5
After the merger, there are quarrels amongst the employees of the erstwhile $X$ ltd, $Y$ ltd, and $Z$ ltd.
An employee does not quarrel with any of the employees from his parent company.
Company :- $X, Y, Z$
Employees: 4, 3 ,5
Any employees in $X$ can have a maximum possible no. of quarrels with the employees of $Y$ ltd. and $Z$ ltd. as given by:
As there are 4 employees in the merged company, who came from $X$;
So, the total number of quarrels involving employees of $X$ company is:
$4×[1×3+1×5]=4×8=32$ quarrels -------(1)
Further, employees of $Y$ & $Z$ ltd. will be involved with quarrels within each other.
The total number of such quarrels:
$=3×[1×5]=5×[1×3]=15$ quarrels --------(2)
From (1) and (2), the total number of quarrels between the employees of three erstwhile companies is:
Hence (C) option is correct.