# CAT 2017 Set-1 | Question: 51

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There are $21$ employees working in a division out of whom $10$ are special-skilled employees $\text{(SE)}$ and the remaining are regular skilled employees $\text{(RE)}$. During the next five months, the division has to complete five projects every month. Out of the $25$ projects, $5$ projects are “challenging”, while the remaining ones are “standard”. Each of the challenging projects has to be completed in different months. Every month, five teams – $\text{T1, T2, T3, T4}$ and $\text{T5}$, work on one project each. $\text{T1, T2, T3, T4}$ nd $\text{T5}$ are allotted the challenging project in the first, second, third, fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest.

In the first month, $\text{T1}$ has one more $\text{SE}$ than $\text{T2, T2}$ has one more $\text{SE}$ than $\text{T3, T3}$ has one more $\text{SE}$ than $\text{T4}$, and $\text{T4}$ has one more $\text{SE}$ than $\text{T5}$. Between two successive months, the composition of the teams changes as follows:

1.  The team allotted the challenging project, gets two $\text{SE}$ from the team which was allotted the challenging project in the previous month. In exchange, one $\text{RE}$ is shifted from the former team to the latter team.
2. After the above exchange, if $\text{T1}$ has any $\text{SE}$ and $\text{T5}$ has any $\text{RE}$, then one $\text{SE}$ is shifted from $\text{T1}$ to $\text{T5}$, and one $\text{RE}$ is shifted from $\text{T5}$ to $\text{T1}$. Also, if $\text{T2}$ has any $\text{SE}$ and $\text{T4}$ has any $\text{RE}$, then one $\text{SE}$ is shifted from $\text{T2}$ to $\text{T4}$, and one $\text{RE}$ is shifted from $\text{T4}$ to $\text{T2}.$

Each standard project has a total of $100$ credit points, while each challenging project has $200$ credit points. The credit points are equally shared between the employees included in that team.

The number of times in which the composition of team $\text{T2}$ and the number of times in which composition of team $\text{T4}$ remained unchanged in two successive months are:

1. $(2,1)$
2. $(1,0)$
3. $(0, 0)$
4. $(1,1)$

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