A certain farm has a group of sheep, some of which are rams (males) an

Another approach :-

It is important to remember that if the ratio of one group to another is x:y, the total number of objects in the two groups together must be a multiple of x + y. So since the ratio of rams to ewes on the farm is 4 to 5, the total number of sheep must be a multiple of 9 (4 parts plus 5 parts). And since the ratio of rams to ewes in the first pen is 4 to 11, the total number of sheep in the first pen must be a multiple of 15 (4 parts plus 11 parts). Since the number of sheep in each pen is the same, the total number of sheep must be a multiple of both 9 and 15.

If we assume that the total number of sheep is 45 (the lowest common multiple of 9 and 15), the number of rams is 20 and the number of ewes is 25 (ratio 4:5).

45/3 = 15, so there are 15 sheep in each pen. Therefore, there are 4 rams and 11 ewes in the first pen (ratio 4:11). This leaves 20 - 4 = 16 rams and 25 - 11 = 14 ewes in the other two pens. Since the second and third pens have the same ratio of rams to ewes, they must have 16/2 = 8 rams and 14/2 = 7 ewes each, for a ratio of 8:7 or 8/7.

let r=rams in pen 3
e=ewes in pen 3
15s=total sheep in pen 1
r+e=15s
r+e is a multiple of 15
plugging in choice A, assume r+e=8 rams+7 ewes=15 sheep
pen 1 must also contain 15 sheep: 4 rams+11 ewes
thus, total farm rams/ewes ratio=20/25=4/5
A

Use weighted averages. You have a "total population" which you have split. This should remind you of weighted averages.

Concentration of rams in total population = 4/9
Concentration of rams in first pen = 4/15
Concentration of rams in second and third pens combined = x (same concentration in both pens)
Since number of sheep in each pen is the same, the weight of first pen:second and third combined = 1:2

1/2 = (x - 4/9)/(4/9 - 4/15)

1/2 *(4/3)*(2/15) + 4/9 = x

8/15 = x

Ratio of rams:ewes = 8:7

Answer (A)

Let's say total 90 sheeps this means rams 40:50 ewes.

Now each group had 30 sheeps.
This implies in group 30*4/15=8 rams and 22 ewes.

Rams left 40-8=32
Ewes left 50-22=28

Now both groups have same ratio this 2r:2e = 32:28

r:e = 8:7

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Did it in a slightly lenghty way, posting it here to showcase one more method in case.

Took LCM of 9, 5 and 11=495
Let 495 be the total number of sheeps
9x=495
x=55
Male Sheeps= 55*4
Female Sheeps=55*5
Dividing 495 by 3, we have 165 sheeps in each pen
First pen is 4:11, 15y=165, y=11
Male in first pen=44
Female in first pen is 121
Balance male sheeps=(55*4)-44=176
Balance Female sheeps= (55*5)-121=154
Since the sheeps are equal in both of remaining pens, male sheeps will be 176/2=88 and female sheeps will be 154/2=77
Ratio=88/77 or 8/7