Question

At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether $65$ dishes. How many guests were present at the party?

• A. $60$
• B. $65$
• C. $90$
• D. None of these

Answer 1

The correct option is A $60$

Let the number of guests be $x$. Then,
number of bowls of rice $=\frac{x}{2}$;
number of bowls of dal $=\frac{x}{3}$;
number of bowls of meat $=\frac{x}{4}$.
$\therefore \frac{x}{2}+\frac{x}{3}+\frac{x}{4}=65\iff \frac{6x+4x+3x}{12}=65\iff 13x=65\times 12$
$\iff x=\left(\frac{65\times 12}{13}\right)=60$