Direction : Study the given information carefully to answer the related…

Concept

In a constraint-grouping puzzle, you do not guess departments — you let the 'closed pair' clues pin down fixed-size groups first, then route everyone else by their colleague and colour restrictions. Two clues here are closed pairs: a person who 'works only with' one specific colleague forms a department of exactly two, and 'only the red and black wearers work together' forms another department of exactly two. Fix those two pairs, and the rest is forced.

Application — fix the closed pairs, step by step

1. T's department is a closed pair: T works only with the green-wearer and is not in marketing, so T's department = {T, green-wearer} exactly, and it is operations or finance (not marketing).

2. The red-wearer and the black-wearer form the OTHER closed pair (only they share a department). Operations bars orange and black, so this red-black department cannot be operations -- it is finance or marketing.

3. T's pair cannot be the red-black pair, since T's colleague wears green, not red or black -- so these are two different departments, and the third department (whichever is left) holds the remaining five people.

4. R wears white, so R is not the red-wearer or the black-wearer -- R is not in the red-black department. R is also not in T's pair: that department holds only T and the green-wearer, and R (white) is not the green-wearer. So R sits in the third, leftover department.

5. R is explicitly not in marketing. Since R is in the leftover department, the leftover department cannot be marketing -- so the leftover department is finance, and the red-black department is therefore marketing.

6. That also fixes T's pair: with finance taken by the leftover department and marketing taken by the red-black pair, the only department left for T's pair is operations.

7. This matches A's own restriction as a cross-check: A avoids operations, and A is in neither T's pair (violet, not green) nor the red-black pair (violet, not red/black) -- so A sits in finance, exactly where the argument above already placed it.

8. R works with G, and R is in finance, so G is in finance too.

9. B works with E, and neither wears black. If either were the red-wearer, the other would have to join the strictly-two-person red-black department as its colleague, becoming the black-wearer -- which is barred. So neither B nor E is in marketing; the same two-person limit on operations keeps them out of T's pair too, so B and E are both in finance.

10. M avoids finance and avoids working with the red-wearer. Since the red-wearer's department is marketing, that rules M out of marketing too. With finance and marketing both closed off, M must be in operations -- and since operations holds only T and the green-wearer, M is the green-wearer.

11. Finance now holds R, G, A, B, E -- five people, exactly the size the leftover department needs. That leaves D and H as the only two people still unplaced, so D and H fill the marketing (red-black) department by elimination.

12. G and D never wear red, so between D and H, D cannot be the red-wearer -- H wears red and D wears black.

13. Purple is barred from finance. Of the remaining uncoloured people, only T sits outside finance -- so T wears purple.

14. E avoids blue and orange, and white, violet, green, red, black, purple are already taken (by R, A, M, H, D, T) -- so E wears pink.

15. G and D avoid orange, so the one remaining colour, orange, goes to B, leaving blue for G.

Result & cross-check

Cross-check every clue against this grid: operations has no orange/black wearer (purple, green); the only red+black pairing is the marketing duo; R sits with G away from marketing; B sits with E and neither wears black; A (violet) avoids operations; M avoids finance and is not with the red-wearer; purple (T) is not in finance; H and E are in different departments; G and D wear neither red nor orange; E wears neither blue nor orange. Every constraint holds, so the marketing department is D and H.