The ratio of the number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents leave, the ratio became 1 : 3. How many people were at the party originally?
The Usual Method
Let the original number of ladies in the party be ‘x’.
Hence, the number of gents = 2x
Hence, number of gents in the party = 2x = 8
Hence, total number of people in the party = 4 + 8 = 12.
Estimated Time to arrive at the answer = 45 seconds.
Since, the original ratio of ladies to gents = 1 : 2, the total number of guests = 1x + 2x = 3x.
Also, the new ratio of ladies to gents = 1 : 3, the total number of guests = 1y + 3y = 4y
Hence the total number of guests should be a multiple of both 3 and should become a multiple of 4 after 4 is subtracted from it. This means that the original number of guest should be a multiple of 3 as well as 4 or a multiple of 12. The only option satisfying this condition is option ‘5’.
Estimated Time to arrive at the answer = 10 seconds.