Question

A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese?

Answer 1

Now the ratio of migration rate for male to the migration rate for the female geese will be 7 : 12

Explanation:

Let the total number of geese in a migration study taken = a

30% of the geese were male then number of males = 0.30a

Then total number of female geese = 0.70a

Let b geese migrated during the study and 20% of them were male then the number of migrated males = 0.20b

Then female geese migrated = b - 0.20b = 0.80b

Then migration rate of male geese during the study =
`\frac{\text{Migrated males}}{\text{Total male geese}}`

=
`(0.20b)/(0.30a)`

=
`(2b)/(3a)`

Similarly migration rat of female geese =
`\frac{\text{Migrated females}}{\text{Total female geese}}`

=
`(0.80b)/(0.70a)`

=
`(8b)/(7a)`

Now the ratio of migration rate for male to the migration rate for the female geese will be =
`((2b)/(3a))/((8b)/(7a))`

=
`(2b)/(3a)* (7a)/(8b)`

=
`(14)/(24)`

=
`(7)/(12)`

Therefore, ratio will be 7 : 12.