One of the days Alex works on is

Lets notate five employees Alex, Bhabha, Cathy, Dilip and Ethan as {A,B,C,D,E} & start by making a representation from Monday to Sunday, in which Mon to sat has 2 spots each to assign and Sunday has 3 spots to assign the employees A, B, C, D, E.

They have given that , A&D work together on Tuesday and Wednesday , all the employees can work only 2 days consecutive and the third day to be non-consecutive , this implies A, D both are not working on Monday & Thursday . It is also given that C is not working on Saturday and Monday, Hence, it implies the remaining B & E must work on Monday as A,D,C are known to be not working on Monday.

It is also known that C has to work three days in which 2 are consecutive but the other is not , and C is known to be not working on Saturday. Therefore, it implies that as 'C' will be working on Thursday, Friday and Sunday only.

So the table will be :

Mon : {B,E}

Tue : {A,D}

Wed : {A,D}

Thu : {---,C}

Fri : {---,C}

Sat : {---,---}

Sun : {----,C,----}

Now, we also know that from the above representation that , 'A' had worked on Tuesday, Wednesday in consecutive , Hence he has to work one more day either of the Fri, Sat, Sunday. But, in the question it is also given that neither B nor C is working with A , and it is also given that A and D work with different people on their 3rd day after Tuesday and Wed. Hence, it implies that the third day of A will be working with the only possibility of E only . Therefore, {A,E} will be a pair on one day among Friday, Sat, Sunday.

As "C" is already placed in Thursday, Friday and Sunday, now "A" cannot be assigned over these days as in the question it is also given that neither B nor C is working with 'A' . Therefore, {A,E} can only be placed on Saturday.

Mon : {B,E}

Tue : {A,D}

Wed : {A,D}

Thu : {---,C}

Fri : {---,C}

Sat : {A,E}

Sun : {----,C,----}

Now, there are 4 empty slots to be filled . From the above representation we can observe that "B" has to be assigned in another 2 slots , D in another 1 slot and E in another 1 slot , then only they satisfy the condition of working for exactly 3 days each.

That is in conclusion {D, E, B, B} has to be assigned in remaining 4 spots available in above representation.

Now, it is also clear that 'E' had worked on Sat, Mon. So he can't work on Sunday because else all 3 days for E would be consecutive . Hence, now the remaining possibilities for 'E' are either Thursday or Friday , but if 'E' plays on Thursday then all 3 working days of 'E' would be non consecutive. Therefore the only possibility for 'E' is to work on Friday so that 'E' can fulfil the criteria of 2 consecutive (Fri,Sat) and one non-consecutive day of work.

Mon : {B,E}

Tue : {A,D}

Wed : {A,D}

Thu : {---,C}

Fri : {E,C}

Sat : {A,E}

Sun : {----,C,----}

Now, from the above we can observe that 'D' had already worked on Tuesday, Wednesday . So 'D' cannot work now on Thursday as the third day needs to be non-consecutive. Therefore the only possibility for 'D' is to work on Sunday.

Mon : {B,E}

Tue : {A,D}

Wed : {A,D}

Thu : {---,C}

Fri : {E,C}

Sat : {A,E}

Sun : {----,C,D}

Now the left out 2 spots has to be assigned to {B,B} . Therefore the final table would be :

Mon : {B,E}

Tue : {A,D}

Wed : {A,D}

Thu : {B,C}

Fri : {E,C}

Sat : {A,E}

Sun : {B,C,D}

Therefore, from the above it is clear that 'Alex' had worked on Tuesday, Wednesday & Saturday. Hence among the given options "Saturday" is the answer.