jmc

Question

A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow when in the sun. Initially, the ratio of green to yellow frogs was 3 : 1. Then 3 green frogs moved to the sunny side and 5 yellow frogs moved to the shady side. Now the ratio is 4 : 1. What is the difference between the number of green frogs and the number of yellow frogs now?

Accepted Answer

Since the original ratio is 3:1 and the new ratio is 4:1, the number of frogs must be a multiple of 12, the only solutions left are (B) and (E). Let's start with 12 frogs: We must have 9 frogs in the shade and 3 frogs in the sun. After the change, there would be 11 frogs in the shade and 1 frog in the sun, which is not a 4:1 ratio. Therefore the answer is: 24.