What is the colour of the tie ?

• From clue 2, C wears a tie. From clue 1, neither B nor Ribeiro wore a white sweater, implying the white sweater is worn by A (since C wears a tie and B is excluded).

• Since A wears the white sweater, A cannot be Ribeiro (clue 1) or Singh (clue 3, as Singh's garment is not white). Thus, A is Kumar.

• Since A is Kumar, and clue 4 states Kumar does not wear a jacket, this is consistent with A wearing a sweater.

• The remaining friends are B and C. The remaining surnames are Ribeiro and Singh. Clue 5 states Ribeiro does not wear black. Clue 3 states Singh's garment is not white (already satisfied as white is with A).

• C wears a tie. If C were Ribeiro, C would not wear black. If C were Singh, C's garment is not white (satisfied). Let's determine B's surname. B cannot be Ribeiro if B wears the white sweater? No, A wears the white sweater. Clue 1 says 'neither B nor Ribeiro wore a white sweater'. This implies B is not the one wearing the white sweater (which is A) and Ribeiro is not the one wearing the white sweater (which is A). This confirms A is not Ribeiro.

• Let's look at colours. A (Kumar) wears White Sweater. Remaining colours: Blue, Black. Remaining garments: Jacket, Tie. Remaining people: B, C. Remaining surnames: Ribeiro, Singh.

• C wears a Tie. B wears a Jacket (since C has Tie, A has Sweater).

• Clue 5: Ribeiro does not wear Black. Clue 3: Singh's garment is not White (A is White, so this doesn't restrict B or C directly regarding White, but we know White is taken).

• Who is Ribeiro? If B is Ribeiro, B (Jacket) cannot be Black, so B is Blue. Then C (Tie) is Black. C would be Singh. Check: Singh (C) wears Black Tie. Is Singh's garment white? No. Is Ribeiro (B) wearing Black? No, Blue. This works.

• If C is Ribeiro, C (Tie) cannot be Black, so C is Blue. Then B (Jacket) is Black. B would be Singh. Check: Singh (B) wears Black Jacket. Is Singh's garment white? No. Is Ribeiro (C) wearing Black? No, Blue. This also seems possible? Wait, let's re-read Clue 1: 'neither B nor Ribeiro wore a white sweater'. This is a negative constraint. It doesn't say B is not Ribeiro. It says the person wearing the white sweater is not B and not Ribeiro. We established A wears the white sweater. So A is not B and A is not Ribeiro. This is consistent.

• Let's re-evaluate the surname assignment. A is Kumar. B and C are Ribeiro and Singh.

• Case 1: B is Ribeiro, C is Singh. B (Jacket) is Ribeiro -> not Black -> Blue. C (Tie) is Singh -> not White (ok) -> Black. Tie is Black.

• Case 2: B is Singh, C is Ribeiro. C (Tie) is Ribeiro -> not Black -> Blue. B (Jacket) is Singh -> not White (ok) -> Black. Tie is Blue.

• Is there a constraint I missed? 'Singh's garment was not white'. In Case 1, Singh (C) wears Black. In Case 2, Singh (B) wears Black. Both satisfy 'not white'.

• Let's check Clue 1 again: 'neither B nor Ribeiro wore a white sweater'. This implies B != wearer of white sweater AND Ribeiro != wearer of white sweater. We know A wears white sweater. So A != B and A != Ribeiro. This is true in both cases.

• Is there a constraint linking surname to garment or colour more tightly?

• Let's look at the options. If the answer is Blue, Case 2 must be the only valid one. Why is Case 1 invalid?

• Let's re-read carefully. 'Singh's garment was not white'.

• Maybe I missed a deduction. Let's look at B. B wears a Jacket.

• If B is Ribeiro, B wears Blue Jacket. C is Singh, C wears Black Tie.

• If B is Singh, B wears Black Jacket. C is Ribeiro, C wears Blue Tie.

• Is there a constraint on B? Clue 1: 'neither B ... wore a white sweater'. This is just saying B is not the white sweater wearer.

• Let's look at the official key: Blue. This implies Case 2 is the correct one. Why is Case 1 wrong?

• Ah, look at Clue 1: 'neither B nor Ribeiro wore a white sweater'. This phrasing often implies that B and Ribeiro are distinct entities from the white sweater wearer, but does it imply B and Ribeiro are distinct from each other? No.

• However, in many such logic puzzles, if a clue says 'Neither X nor Y did Z', and we find Z was done by W, it just confirms W is not X and W is not Y.

• Let's check if 'Singh's garment was not white' eliminates Case 1? In Case 1, Singh is C, wearing Black. Not white. Valid.

• Let's check if 'Ribeiro does not like to wear the black colour' eliminates Case 1? In Case 1, Ribeiro is B, wearing Blue. Not black. Valid.

• Is there a constraint I am missing?

• Let's re-read Clue 3: 'Singh's garment was not white'.

• Let's re-read Clue 5: 'Ribeiro does not like to wear the black colour'.

• Let's re-read Clue 4: 'Kumar does not wear a jacket'. A is Kumar, wears Sweater. Valid.

• Let's re-read Clue 2: 'C wore a tie'.

• Let's re-read Clue 1: 'neither B nor Ribeiro wore a white sweater'.

• Perhaps the key lies in 'Singh's garment was not white'. If Singh wore Black, is that allowed? Yes.

• Wait, look at the colours: Blue, White, Black.

• If Case 1 is valid, the tie is Black. If Case 2 is valid, the tie is Blue. The question asks for the colour of the tie. The key is Blue. This means Case 1 must be invalid.

• Why is Case 1 invalid?

• In Case 1: B=Ribeiro (Blue Jacket), C=Singh (Black Tie), A=Kumar (White Sweater).

• In Case 2: B=Singh (Black Jacket), C=Ribeiro (Blue Tie), A=Kumar (White Sweater).

• Is there a constraint that Singh cannot wear Black? No.

• Is there a constraint that Ribeiro cannot wear Blue? No.

• Let's look at Clue 1 again. 'neither B nor Ribeiro wore a white sweater'.

• Could it be that B and Ribeiro are the same person? If B is Ribeiro, then 'neither B nor Ribeiro' is redundant but true.

• If B is Singh, then B is not Ribeiro.

• Is there a standard convention?

• Let's check the source or similar problems. Often, 'Singh's garment was not white' is a distractor if White is already assigned.

• Let's look at the names: A, B, C. Surnames: Ribeiro, Kumar, Singh.

• A is Kumar.

• Remaining: B, C. Surnames: Ribeiro, Singh.

• If B is Ribeiro, C is Singh.

• If B is Singh, C is Ribeiro.

• Clue 5: Ribeiro != Black.

• Clue 3: Singh != White.

• In Case 1 (B=Rib, C=Sing): B(Jacket) != Black -> Blue. C(Tie) = Black. Singh(C) != White (Black is not White). OK.

• In Case 2 (B=Sing, C=Rib): C(Tie) != Black -> Blue. B(Jacket) = Black. Singh(B) != White (Black is not White). OK.

• Both seem logically valid based on the text provided. However, the official key is Blue. This implies there is a constraint I am overlooking or a specific interpretation.

• Re-reading Clue 1: 'neither B nor Ribeiro wore a white sweater'.

• If B were Ribeiro, the statement 'neither B nor Ribeiro' is just 'neither B'.

• If B is not Ribeiro, it's 'neither B nor Ribeiro'.

• Is it possible that 'Singh's garment was not white' implies Singh's garment is NOT the one that is white, but also implies something else? No.

• Let's assume the question implies a unique solution. If both are valid, the answer would be 'Cannot be determined'. But the key is Blue.

• Let's look for a subtle error in Case 1.

• In Case 1, C is Singh. C wears a Tie. The tie is Black.

• In Case 2, C is Ribeiro. C wears a Tie. The tie is Blue.

• Is there a constraint on C? No.

• Is there a constraint on the Tie? No.

• Wait! Look at Clue 1 again. 'neither B nor Ribeiro wore a white sweater'.

• This implies that the person who wore the white sweater is NOT B and NOT Ribeiro.

• We know A wore the white sweater. So A is not B and A is not Ribeiro.

• This is always true since A, B, C are distinct.

• Is it possible that 'Ribeiro' and 'B' are meant to be distinct? No.

• Let's check the UPSC answer key explanation if available online (simulated).

• Common trap: 'Singh's garment was not white'. If Singh wore Black, is that 'not white'? Yes.

• However, in some logic puzzles, if a colour is not specified as 'not white', it might be assumed? No.

• Let's look at the options again. (a) Black, (b) Blue, (c) White, (d) Cannot be determined.

• If the answer is Blue, Case 2 is the intended path. Why is Case 1 rejected?

• Perhaps 'Ribeiro does not like to wear the black colour' is interpreted as 'Ribeiro wears Blue or White'.

• 'Singh's garment was not white' is interpreted as 'Singh wears Blue or Black'.

• In Case 1: Ribeiro (B) wears Blue. Singh (C) wears Black.

• In Case 2: Ribeiro (C) wears Blue. Singh (B) wears Black.

• Both fit.

• Is there a constraint that B cannot be Singh? No.

• Is there a constraint that C cannot be Ribeiro? No.

• Let's look at the phrasing 'neither B nor Ribeiro wore a white sweater'.

• If B is Ribeiro, the phrase is 'neither B nor B wore...'.

• If B is not Ribeiro, the phrase is 'neither B nor Ribeiro wore...'.

• Usually, such phrasing implies B and Ribeiro are two different people? No, 'neither John nor John' is valid English but odd. 'Neither John nor Mary' implies distinct. If the author intended B and Ribeiro to be distinct, then B cannot be Ribeiro.

• If B != Ribeiro, then B must be Singh (since A is Kumar).

• If B is Singh, then C is Ribeiro.

• This leads to Case 2.

• In Case 2: C is Ribeiro. Ribeiro (C) wears Tie. Ribeiro does not wear Black. So Tie is Blue (since White is with A).

• Therefore, the tie is Blue.

• This interpretation (that 'neither X nor Y' implies X and Y are distinct entities in the context of the puzzle's constraints) forces B to be Singh and C to be Ribeiro.

• Thus, C (Ribeiro) wears the Tie. Ribeiro does not wear Black. White is taken by A. So C wears Blue.

• The tie is Blue.