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? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]A. 1/4B. 7/12C. 2/3D. 7/8E. 8/7

Answer 1

(B).
`(7)/(12)`

Explanation:

In the question,

Let the total number of geese be = 100x

Number of Male geese = 30% = 30x

Number of Female Geese = 70x

Let us say 'kx' geese migrated from these geese.

Number of migrated Male geese = 20% of kx = kx/5

Number of migrated Female geese = 4kx/5

So,

Migration rate of Male geese is given by,

`(((kx)/(5)))/(30x)`

Migration rate of Female geese is given by,

`(((4kx)/(5)))/(70x)`

So,

The ratio of Migration rate of Male geese to that of Female geese is given by,

`(\left[(((kx)/(5)))/(30x)\right])/(\left[(((4kx)/(5)))/(70x)\right])=(350)/(4* 150)=(7)/(12)`

Therefore, the ratio of the rate of migration of Male geese to that of Female geese is,

`(7)/(12)`

Hence, the correct option is (B).