At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs? Choose the correct choice from the following answers:
A) 25% B) 10% or 60% C) 50% D) 55% E) 70%
Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)   The initial ratio for L:A:E :: 2:4:8   Initial Total dogs = 14X ( x assumed; 2+4+8= 
<gadget id="calculator">2+4+8</gadget>
<output>14</output>
14), Since the total dogs are less than 30 therefore initial total value has to be 14   L= 2, A = 4 E = 8   L:A= 2:5   This ratio doubles   Hence New Dog count is   L= 4 , A = 4 E= X: Also 4+4+x&lt;30   We need to Find X*100/(4+4+X)   Now it says that new percentage of little dogs and Average dogs is an integer   %L = 4*100/(8+x) %A = 4*100/(8+x); Only Value for X is 2 or 12 ; 9+x&lt;30 and % integer   Therefore, Enormus Dogs % is = 12*100/(20) or 2*100/20 = 60% or 10%   10% or 60%
<result>B</result>
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?