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?

Answer 1

Finding the total number of guests at the party:

Let the total number of guests be $x$.

Therefore,

Number of bowls of dal $=\frac{x}{2}$

Number of bowls of rice $=\frac{x}{3}$

Number of bowls of meat $=\frac{x}{4}$

Now, according to question , there are altogether $65$ dishes.

So we have ,

Number of bowls of dal $+$Number of bowls of rice $+$Number of bowls of meat$=65$

$\frac{x}{2}+$$\frac{x}{3}+$$\frac{x}{4}=65$

$$\begin{gathered} \Rightarrow \frac{6x+4x+3x}{12}=65 \\ \Rightarrow \frac{13x}{12}=65 \\ \Rightarrow x=\frac{65x12}{13} \\ \Rightarrow x=60 \end{gathered}$$

Hence, the total number of guests at the party is$60$.