The number of cows in a farm was 60% of the number of the goats. After 80 goats were taken out of the farm, the number of goats became 60% of the number of cows in the farm.

(a) how many cows were there in the farm?

(b) what is the percentage of the goats were moved out of the farm?

Before:

The number of goats = 60%

The number of cows = 100%

Using ratio

Cows : Goats

60 : 100 reduced to simplest term

C:G

3:5

After

The number of cows = 100%

The number of goats = 60%

Using ratio

C:G

100:60 reduced to simplest term

C:G

5:3

Number of cows remained constant. Therefore find the common multiple.

Before

C:G

15:25

After

C:G

15:9

Find the difference in the units of goats

(a) 25 - 19 = 16

16 units = 80

1 unit = 5

15 units (cows) = 5 x 15 = 75

There were 75 cows.

(B)

Number of goats at first

25 units = 5 x 25 = 125

Therefore percentage = 80/125 x 100

= 64%