AMO 2027 Grades 4-5 SET 18 - Self-study Question 14

Billy and Phil the rabbits are in separate cages. The ratio of the number of carrots in Billy’s cage to Phil’s cage was 3 : 4. After some carrots from Phil’s cage were transferred to Billy’s cage, the ratio of the number of carrots in Billy’s cage to Phil’s cage became 2 : 1. What is the smallest possible number of carrots that were transferred?

Count whole carrots; carrots are transferred without splitting and none are added or removed.