Question

At a party, colas, squash and fruit juice were offered to guests. A fourth of the guests drank colas, a third drank squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?

Answer 1

Let the total number of guests be x .
Therefore, the number of guests, who drank colas, would be \[\frac{1}{4}x . \]
The number of guests, who drank squash, would be \[\frac{1}{3}x . \]
The number of guests, who drank fruit juice, would be \[\frac{2}{5}x . \]
The number of guests, who did not drink, would be 3 . 
According to the question, 
\[x - (\frac{x}{4} + \frac{x}{3} + \frac{2x}{5}) = 3\]
or \[ \frac{60x - 15x - 20x - 24x}{60} = 3\]
or x = 180
Thus, total number of guests = 180.