Let there be g geese, of which 0.3g are male and 0.7g are female
Lets say m geese migrated, 0.2m are male and 0.8m are female

Migration Rate Male = 0.2m / 0.3g = (2/3)*(m/g)
Migration Rate Female = 0.8m / 0.7g = (8/7)*(m/g)

Ratio of migration rates = (2/3) / (8/7) = 7/12

Answer is (b)
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Let' take the Number of geese to be 100.

Male = 30. Female = 70.

Now the second part of the Q, Let's take the Number migrated to be 20.

So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *20 = 4 Geese (Males)

And now we know out of the total 20 geese , 4 are male , then 16 have to be female.

Now the ratio part , Male Geese Ratios = 4/30 = 2/15. - A

Female Geese Ratios =16/70=8/35 - B

Cross Multiply Equations A and B and you get =7/12 .

Ans B

say 100 are geese.. 30% means 30 are male and 70 are female.

Now x geese migrates,
Therefore \(\frac{x}{5}\) are male (since 20% of migrating geeses are male) and hence \(\frac{4x}{5}\) are female

Therefore \(\frac{Migration rate male}{Migration rate female}\) = {(x/5)/30} / {(4x/5)/70}

Solving we get, 7/12 as answer.

Consider Kudos if the post helped.

0.2 * (0.3x) is a problem. The questions says that 20% of the geese migrating were males. It doesn't say that 20% of males migrated.

Sp if there were 100 geese in all, 30 were males. The question does NOT say that 20% of these 30 migrated.

Say, if half the total geese migrated, 50 migrated. Out of these 50, 20% were male i.e. 10 were male.

SO we need to take 20% of migrated geese, not the 20% of male population.

Does this sort out your problem?
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We can let t = the total number of geese before migration; thus, the number of male geese = 0.3t and the number of female geese = 0.7t. If we let the number of migrating geese = m, then the number of male migrating geese = 0.2m and the number of female migrating geese = 0.8m.

Thus, the migration rate for the male geese is 0.2m/0.3t = 2m/3t and the migration rate for the female geese is 0.8m/0.7t = 8m/7t.

Thus, the ratio of male migration rate to female migration rate is:

(2m/3t)/(8m/7t) = (7t x 2m)/(3t x 8m) = (14mt)/(24mt) = 14/24 = 7/12.

Answer: B
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What level question is this?

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Great explanation! Can someone quickly point out why you divide (1/3) by (4/7) in order to take the ratio of those?

Thanks

Let's say 30 male and 70 female studied. Let' say, of 100 geese, 60 were migrating. 12 males migrating, 48 female migrating.
Male rate: 12/30=2/5
Female rate: 48/70=24/35
Male/Female=5*24/2*35= 7/12