Ducks and Penguins

[rahulvsd]

Two expedition groups, the Ducks and the Penguins, were each delivered x kilograms of supplies. When the members actually showed up, it turned out that there were four fewer people in the Ducks contingent. The Ducks gave y kilograms of their supplies to the Penguins, so that each group would have the same weight of supplies per person. With 20 people in the total expedition, what percent of the Ducks initial allocation was transferred?
A 10%
B 12%
C 15%
D 18%
E 20%

[spoiler]OA: E. My doubt is in the wording of the question. What do you mean four fewer people in the ducks contingent. Is it four less than penguins or four less than the initial number of people part of the duck group.[/spoiler]

[rijul007]

When the members actually showed up, it turned out that there were four fewer people in the Ducks contingent

If no of members in duck was a
No of members in penguins = a+4

With 20 people in the total expedition

a+a+4 = 20
a = 8

The Ducks gave y kilograms of their supplies to the Penguins, so that each group would have the same weight of supplies per person

(x-y)/8 = (x+y)/12
solve and we get
x = 5y

Percent of the ducks initial allocation that was transferred = (y/5y) * 100 = 20 %

Option E

[GmatMathPro]

My doubt is in the wording of the question. What do you mean four fewer people in the ducks contingent. Is it four less than penguins or four less than the initial number of people part of the duck group.

It means the ducks have four fewer people than the penguins. If you assume it means four fewer than were expected for the ducks, you can't solve the problem. For example, it could be that they expected 14 ducks and 10 penguins, but only 10 ducks and 10 penguins showed up, in which case y=0, and the answer would be 0%. Or it could be that they expected 19 penguins and 5 ducks, but 19 penguins and 1 duck showed up in which case the answer would be 90%

[user123321]

since from question...

Two expedition groups, the Ducks and the Penguins, were each delivered x kilograms of supplies.

and also

The Ducks gave y kilograms of their supplies to the Penguins, so that each group would have the same weight of supplies per person.

the number of people in both contigents should be same before they showed up.

so in one group it should be 8 and in another it should be 12.
let x is given initially to each group then each should get x/12 of supplies.
since 4 people didnt showed up, the remaining 4x/12 of supplies should be distributed to all 20.
so each will get and extra of 4x/(20*12) = x/60
the 8 member group should use 8*x/60 and give remaining 12*x/60 to other group
=> amount given to other group by/initial amount = 12*x/(60*x) = 0.2 = 20%

user123321