Discussion Forum

At a farm, there are hens, cows and bullocks, and the keepers to look after them. There are 69 heads less than legs; the number of cows and hens is the same and there is one keeper per ten birds and cattle. The total number of hens plus cows and bullocks, and their keepers does not exceed 50. How many cows are there?

Answer:

Explanation:

 Let H, C, B and K represent the number of hens, cows, bullocks and keepers respectively. Then, as given, we have:

H + C + B + K < 50 .......(i)

 C = 2B  .........(ii)

C = H .........(iii)

$K= \frac{H+C+B}{10}$ .........(iv)

From , (ii),(iii),(iv), we have:

10K = H + C+ B  <=> 10K = 2C + B  = 2 X 2B  <=> 10K = 5B

B = 2K

So, B = 2K ,C = 2B =4K , H = C 4K

Total number of heads =  H + C + B + K .

Total number of legs = 2H + 4C + 4B + 2K

(2H + 4C + 4B + 2K) - (H + C + B + K ) = 69

H + 3C + 3B + K = 69

4K + 12K + 6K + K =69

K = 3

Hence number of cows = C = 4K =(4 X 3) = 12