# Difficult Algebra Solved QuestionAptitude Discussion

 Q. Three business entities $X$ Ltd, $Y$ Ltd. and $Z$ Ltd, with 4, 3 and 5 employees respectively, merged into $XYZ$ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur. After two years, on the question of management decisions on the new venture at Jaipur, the employees started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there is no quarrel among the employees of the erstwhile (i.e. former)  $X$ Ltd, $Y$ Ltd and $Z$ Ltd, what could be the maximum number of quarrels that can take place within $XYZ$ Ltd?
 ✖ A. 31 ✖ B. 53 ✔ C. 47 ✖ D. 41

Solution:
Option(C) is correct

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:

$1×3+1×5$

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:

$=32+15=47$ quarrels.

Hence (C) option is correct.