A Dinner Party

         At a dinner party every two guests used a dish of rice between them. Every three guests used a dish of dhal and every four used a dish of meat between them. 

There were altogether 65 dishes.

How many guests were present?

Answer :   60 – Let X equal the number of guests. The number of dishes shared:

X/2 + X/3 + X/ 4 = 65

6X + 4X + 3X = 65 x12

13x = 65 x 12

X = 65x 12 /13 = 60