Let total number of geese be G
Therefore, number of geese that are male = 30% of G = 0.3*G

Assuming a goose can be either a goose or a gander (hehe) this means that 70% of the total number of geese are female
So number of female geese = 0.7*G

Let the number of geese that migrated be M
Therefore, number of male migrating geese = 20% of M = 0.2*M

Therefore number of female migrating geese = 0.8*M


Using the formula for migration rate provided:

Migration rate for male geese = 0.2*M / 0.3*G

Migration rate for female geese = 0.8*M / 0.7*G

Therefore ratio of the 2 rates = 0.2*M * 0.7*G / 0.3*G *0.8*M

= 14/24

= 7 /12

Pick B

Let the total number of geese be n.

Male population becomes 30n/100 as given in the question
female becomes = 1- 30n/100 = 70n/100

Let the migrating population be x

male population migrating = 20x/100
female population migrating = 80x/100

male ratio = (20x/100)/(30n/100) = 2x/3n
female ratio = (80x/100)/(70n/100) = 8x/7n

overall ratio = 2x/3n / 8x/7n = 2/3 * 7/8 = 7/12 (B)

Please correct me if I have done any step wrong.

When dealing with percentages of an unspecified value, many people find it quicker/easier to pick numbers than to use algebra.

When dealing with a percent of an unknown value, pick 100. So, let the number of geese be 100. 30 are males while 70 are females.

Some unknown number of geese migrated, and 20% of them were male. Suppose that 50 geese migrated. Then, 10 were males while 40 were females. So 10 out of 30 male geese migrated while 40 out of 70 female geese migrated.

So the migration rate for male geese is 1/3 while the migration rate for female geese is 4/7. The ratio is (1/3)/(4/7) or 7/12.

Choose B.