How many guests were there in the party when 1/4 cola,1/3 squash,2/5 fruit juice,3 no drinks taken?

Question

At a party, Colas, squash and fruit juice were offered to the guests. One fourth of the guests drank cola, one third drank squash, two fifths drank fruit juice and 3 people did not drank anything. How many guests were there in the party

Answer 1

We know that n/4+n/3+2n/5+3=n, where n=number of guests. So the lowest common denominator of 3, 4 and 5 is 60, so multiply through by 60: 15n+20n+24n+180=60n. Therefore 60-(15+20+24)n=180 and n=180, so there were 180 guests. Check: 45 drank cola, 60 drank squash, 72 drank fruit juice and 3 didn't drink=180.