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At a dinner party , every two guests shared a bowl of rice between them , every three guests shared a bowl of vegetable among them and every four shared a bowl of meat among them . There were altogether 65 bowls. How many guests were present at the party?

At a dinner party , every two guests shared a bowl of rice between them , every three guests shared a bowl of vegetable among them and every four shared a bowl of meat among them . There were altogether 65 bowls. How many guests were present at the party? Correct Answer 60

Let the total number of guests be x. Then, Number of bowls of rice = 2x​ Number of bowls of dal = 3x​ Number of bowls of meat = 4x​ ∴2x​ + 3x​ + 4x​ = 65 ⟹126x + 4x + 3x​ = 65⟹1213x​ = 65⟹x = 60 Therefore, 60 guests were present at the party

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