Question:
Chetan invited five friends—Ritwik, Avantika, Darshan, Parul and Shweta—to his birthday. Each gifted a different article: jacket, watch, shirt, video game, headphone. In return, Chetan gave each a different article: goggles, bag, pen, mobile case, diary.
[2pt]
i) Avantika gifted the shirt but did not receive a bag.
ii) Shweta did not gift the headphone but received the mobile case.
iii) Neither Ritwik nor Darshan gifted the jacket; whoever gifted it received the goggles in return.
iv) The person who gifted the video game received a diary or a bag.
v) Darshan did not gift a watch but received a pen in return.
vi) Shweta did not gift a video game and Ritwik did not receive a diary.
\textbf{Who gifted the headphones?}
Chetan invited five friends—Ritwik, Avantika, Darshan, Parul and Shweta—to his birthday. Each gifted a different article: jacket, watch, shirt, video game, headphone. In return, Chetan gave each a different article: goggles, bag, pen, mobile case, diary.
[2pt] i) Avantika gifted the shirt but did not receive a bag.
ii) Shweta did not gift the headphone but received the mobile case.
iii) Neither Ritwik nor Darshan gifted the jacket; whoever gifted it received the goggles in return.
iv) The person who gifted the video game received a diary or a bag.
v) Darshan did not gift a watch but received a pen in return.
vi) Shweta did not gift a video game and Ritwik did not receive a diary.
\textbf{Who gifted the headphones?}
[2pt] i) Avantika gifted the shirt but did not receive a bag.
ii) Shweta did not gift the headphone but received the mobile case.
iii) Neither Ritwik nor Darshan gifted the jacket; whoever gifted it received the goggles in return.
iv) The person who gifted the video game received a diary or a bag.
v) Darshan did not gift a watch but received a pen in return.
vi) Shweta did not gift a video game and Ritwik did not receive a diary.
\textbf{Who gifted the headphones?}
Show Hint
After fixing any “gift \(\Rightarrow\) specific return” pair (here, jacket \(\Rightarrow\) goggles), use remaining returns to force who can take the conditional pair (video game \(\Rightarrow\) diary/bag), then finish by elimination.
Updated On: Aug 14, 2025
- Shweta
- Ritwik
- Darshan
- Parul
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Fix direct information.
Avantika \(\rightarrow\) shirt, return \(\neq\) bag. (i)
Shweta \(\rightarrow\) return mobile case, gift \(\neq\) headphone, \(\neq\) video game. (ii, vi)
Darshan \(\rightarrow\) return pen, gift \(\neq\) watch. (v) Step 2: Determine jacket and its return.
From (iii): Ritwik \(\neq\) jacket, Darshan \(\neq\) jacket; Avantika already shirt \(\Rightarrow\) Parul must have gifted the jacket.
Hence Parul’s return \(=\) goggles. (iii) Step 3: Determine video game and its return.
By (iv), video-game giver gets diary or bag. Ritwik cannot get diary (vi). Also Avantika cannot get bag (i), while Shweta already has mobile case, Parul goggles, Darshan pen.
Thus the only way to satisfy (iv) is Ritwik = video game with return bag. Step 4: Assign remaining gifts.
Gifts used so far: \(\{\)shirt (Avantika), jacket (Parul), video game (Ritwik)\(\}\). Left: \(\{\)watch, headphone\(\}\) for \(\{\)Shweta, Darshan\(\}\).
Since Darshan \(\neq\) watch (v), \(\Rightarrow\) Darshan = headphones and Shweta = watch. \[ \boxed{\text{Darshan gifted the headphones.}} \]
Avantika \(\rightarrow\) shirt, return \(\neq\) bag. (i)
Shweta \(\rightarrow\) return mobile case, gift \(\neq\) headphone, \(\neq\) video game. (ii, vi)
Darshan \(\rightarrow\) return pen, gift \(\neq\) watch. (v) Step 2: Determine jacket and its return.
From (iii): Ritwik \(\neq\) jacket, Darshan \(\neq\) jacket; Avantika already shirt \(\Rightarrow\) Parul must have gifted the jacket.
Hence Parul’s return \(=\) goggles. (iii) Step 3: Determine video game and its return.
By (iv), video-game giver gets diary or bag. Ritwik cannot get diary (vi). Also Avantika cannot get bag (i), while Shweta already has mobile case, Parul goggles, Darshan pen.
Thus the only way to satisfy (iv) is Ritwik = video game with return bag. Step 4: Assign remaining gifts.
Gifts used so far: \(\{\)shirt (Avantika), jacket (Parul), video game (Ritwik)\(\}\). Left: \(\{\)watch, headphone\(\}\) for \(\{\)Shweta, Darshan\(\}\).
Since Darshan \(\neq\) watch (v), \(\Rightarrow\) Darshan = headphones and Shweta = watch. \[ \boxed{\text{Darshan gifted the headphones.}} \]
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