Question

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?

Answer 1

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%